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------------------------------------------------------------------------
Map identifier: Mp00306

------------------------------------------------------------------------
Map name: rowmotion cycle type

------------------------------------------------------------------------
Domain: Posets

------------------------------------------------------------------------
Codomain: Integer partitions

------------------------------------------------------------------------
Description: The cycle type of rowmotion on the order ideals of a poset.

------------------------------------------------------------------------
References: 

------------------------------------------------------------------------
Code:

def mapping(P):
    P = P.canonical_label()
    J = P.antichains(lambda a: frozenset(P.order_ideal(a)))
    if J.cardinality() > 500:
        raise ValueError("Poset has too many order ideals for this map")
    D = DiscreteDynamicalSystem(J, lambda I: P.rowmotion(I), inverse=True, is_finite=True)
    return Partition(sorted([len(o) for o in D.cycles()], reverse=True))


------------------------------------------------------------------------
Map images:

([],1)                                                                        => [2]
([],2)                                                                        => [2,2]
([(0,1)],2)                                                                   => [3]
([],3)                                                                        => [2,2,2,2]
([(1,2)],3)                                                                   => [6]
([(0,1),(0,2)],3)                                                             => [3,2]
([(0,2),(2,1)],3)                                                             => [4]
([(0,2),(1,2)],3)                                                             => [3,2]
([],4)                                                                        => [2,2,2,2,2,2,2,2]
([(2,3)],4)                                                                   => [6,6]
([(1,2),(1,3)],4)                                                             => [6,2,2]
([(0,1),(0,2),(0,3)],4)                                                       => [3,2,2,2]
([(0,2),(0,3),(3,1)],4)                                                       => [7]
([(0,1),(0,2),(1,3),(2,3)],4)                                                 => [4,2]
([(1,2),(2,3)],4)                                                             => [4,4]
([(0,3),(3,1),(3,2)],4)                                                       => [4,2]
([(1,3),(2,3)],4)                                                             => [6,2,2]
([(0,3),(1,3),(3,2)],4)                                                       => [4,2]
([(0,3),(1,3),(2,3)],4)                                                       => [3,2,2,2]
([(0,3),(1,2)],4)                                                             => [3,3,3]
([(0,3),(1,2),(1,3)],4)                                                       => [5,3]
([(0,2),(0,3),(1,2),(1,3)],4)                                                 => [3,2,2]
([(0,3),(2,1),(3,2)],4)                                                       => [5]
([(0,3),(1,2),(2,3)],4)                                                       => [7]
([],5)                                                                        => [2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2]
([(3,4)],5)                                                                   => [6,6,6,6]
([(2,3),(2,4)],5)                                                             => [6,6,2,2,2,2]
([(1,2),(1,3),(1,4)],5)                                                       => [6,2,2,2,2,2,2]
([(0,1),(0,2),(0,3),(0,4)],5)                                                 => [3,2,2,2,2,2,2,2]
([(0,2),(0,3),(0,4),(4,1)],5)                                                 => [7,6]
([(0,1),(0,2),(0,3),(2,4),(3,4)],5)                                           => [7,2,2]
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)                                     => [4,2,2,2]
([(1,3),(1,4),(4,2)],5)                                                       => [14]
([(0,3),(0,4),(4,1),(4,2)],5)                                                 => [7,2,2]
([(1,2),(1,3),(2,4),(3,4)],5)                                                 => [4,4,2,2]
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)                                           => [5,2]
([(0,3),(0,4),(3,2),(4,1)],5)                                                 => [4,3,3]
([(0,2),(0,3),(2,4),(3,1),(3,4)],5)                                           => [5,4]
([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)                                     => [4,2,2]
([(2,3),(3,4)],5)                                                             => [4,4,4,4]
([(1,4),(4,2),(4,3)],5)                                                       => [4,4,2,2]
([(0,4),(4,1),(4,2),(4,3)],5)                                                 => [4,2,2,2]
([(2,4),(3,4)],5)                                                             => [6,6,2,2,2,2]
([(1,4),(2,4),(4,3)],5)                                                       => [4,4,2,2]
([(0,4),(1,4),(4,2),(4,3)],5)                                                 => [4,2,2]
([(1,4),(2,4),(3,4)],5)                                                       => [6,2,2,2,2,2,2]
([(0,4),(1,4),(2,4),(4,3)],5)                                                 => [4,2,2,2]
([(0,4),(1,4),(2,4),(3,4)],5)                                                 => [3,2,2,2,2,2,2,2]
([(0,4),(1,4),(2,3)],5)                                                       => [6,3,3,3]
([(0,4),(1,3),(2,3),(2,4)],5)                                                 => [8,3,2]
([(0,4),(1,3),(1,4),(2,3),(2,4)],5)                                           => [5,3,2,2]
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)                                     => [3,2,2,2,2]
([(0,4),(1,4),(2,3),(4,2)],5)                                                 => [5,2]
([(0,4),(1,3),(2,3),(3,4)],5)                                                 => [7,2,2]
([(0,4),(1,4),(2,3),(2,4)],5)                                                 => [6,5,3]
([(0,4),(1,4),(2,3),(3,4)],5)                                                 => [7,6]
([(1,4),(2,3)],5)                                                             => [6,6,6]
([(1,4),(2,3),(2,4)],5)                                                       => [10,6]
([(0,4),(1,2),(1,4),(2,3)],5)                                                 => [8,3]
([(0,3),(1,2),(1,3),(2,4),(3,4)],5)                                           => [5,4]
([(1,3),(1,4),(2,3),(2,4)],5)                                                 => [6,2,2,2,2]
([(0,3),(0,4),(1,3),(1,4),(4,2)],5)                                           => [7,2]
([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5)                                     => [4,2,2]
([(0,4),(1,2),(1,4),(4,3)],5)                                                 => [10]
([(0,4),(1,2),(1,3)],5)                                                       => [6,3,3,3]
([(0,4),(1,2),(1,3),(1,4)],5)                                                 => [6,5,3]
([(0,2),(0,4),(3,1),(4,3)],5)                                                 => [5,4]
([(0,4),(1,2),(1,3),(3,4)],5)                                                 => [10,2]
([(0,2),(0,3),(1,4),(2,4),(3,1)],5)                                           => [8]
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)                                           => [7,2,2]
([(0,3),(0,4),(1,2),(1,4)],5)                                                 => [8,3,2]
([(0,3),(0,4),(1,2),(1,3),(1,4)],5)                                           => [5,3,2,2]
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4)],5)                                     => [3,2,2,2,2]
([(0,3),(0,4),(1,2),(1,3),(2,4)],5)                                           => [10]
([(0,3),(1,2),(1,4),(3,4)],5)                                                 => [8,3]
([(0,3),(0,4),(1,2),(2,3),(2,4)],5)                                           => [7,2]
([(1,4),(3,2),(4,3)],5)                                                       => [10]
([(0,3),(3,4),(4,1),(4,2)],5)                                                 => [5,2]
([(1,4),(2,3),(3,4)],5)                                                       => [14]
([(0,4),(1,2),(2,4),(4,3)],5)                                                 => [8]
([(0,3),(1,4),(4,2)],5)                                                       => [12]
([(0,4),(3,2),(4,1),(4,3)],5)                                                 => [8]
([(0,4),(1,2),(2,3),(2,4)],5)                                                 => [10]
([(0,4),(2,3),(3,1),(4,2)],5)                                                 => [6]
([(0,3),(1,2),(2,4),(3,4)],5)                                                 => [4,3,3]
([(0,4),(1,2),(2,3),(3,4)],5)                                                 => [5,4]
([(0,3),(1,4),(2,4),(3,1),(3,2)],5)                                           => [5,2]
([],6)                                                                        => [2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2]
([(4,5)],6)                                                                   => [6,6,6,6,6,6,6,6]
([(3,4),(3,5)],6)                                                             => [6,6,6,6,2,2,2,2,2,2,2,2]
([(2,3),(2,4),(2,5)],6)                                                       => [6,6,2,2,2,2,2,2,2,2,2,2,2,2]
([(1,2),(1,3),(1,4),(1,5)],6)                                                 => [6,2,2,2,2,2,2,2,2,2,2,2,2,2,2]
([(0,1),(0,2),(0,3),(0,4),(0,5)],6)                                           => [3,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2]
([(0,2),(0,3),(0,4),(0,5),(5,1)],6)                                           => [7,6,6,6]
([(0,1),(0,2),(0,3),(0,4),(3,5),(4,5)],6)                                     => [7,6,2,2,2,2]
([(0,1),(0,2),(0,3),(0,4),(2,5),(3,5),(4,5)],6)                               => [7,2,2,2,2,2,2]
([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)                         => [4,2,2,2,2,2,2,2]
([(1,3),(1,4),(1,5),(5,2)],6)                                                 => [14,6,6]
([(0,3),(0,4),(0,5),(5,1),(5,2)],6)                                           => [7,6,2,2,2,2]
([(1,2),(1,3),(1,4),(3,5),(4,5)],6)                                           => [14,2,2,2,2]
([(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6)                                     => [4,4,2,2,2,2,2,2]
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,5),(5,1)],6)                               => [5,2,2,2]
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,1)],6)                                     => [6,4,3,3]
([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5)],6)                               => [8,4,2]
([(0,1),(0,2),(0,3),(1,5),(2,4),(2,5),(3,4),(3,5)],6)                         => [5,4,2,2]
([(0,1),(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)                   => [4,2,2,2,2]
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,1),(4,5)],6)                               => [6,5,4]
([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)                               => [8,2,2]
([(0,2),(0,3),(0,4),(3,5),(4,5),(5,1)],6)                                     => [5,4,2,2]
([(0,3),(0,4),(0,5),(4,2),(5,1)],6)                                           => [7,6,6]
([(0,2),(0,3),(0,4),(3,5),(4,1),(4,5)],6)                                     => [10,7]
([(0,1),(0,2),(0,3),(2,4),(2,5),(3,4),(3,5)],6)                               => [7,2,2,2,2]
([(2,3),(2,4),(4,5)],6)                                                       => [14,14]
([(1,4),(1,5),(5,2),(5,3)],6)                                                 => [14,2,2,2,2]
([(0,4),(0,5),(5,1),(5,2),(5,3)],6)                                           => [7,2,2,2,2,2,2]
([(2,3),(2,4),(3,5),(4,5)],6)                                                 => [4,4,4,4,2,2,2,2]
([(1,2),(1,3),(2,5),(3,5),(5,4)],6)                                           => [10,2,2]
([(0,3),(0,4),(3,5),(4,5),(5,1),(5,2)],6)                                     => [5,2,2]
([(1,4),(1,5),(4,3),(5,2)],6)                                                 => [6,6,4,4]
([(1,3),(1,4),(3,5),(4,2),(4,5)],6)                                           => [10,4,4]
([(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6)                                     => [4,4,2,2,2,2]
([(0,2),(0,3),(2,4),(2,5),(3,4),(3,5),(5,1)],6)                               => [8,2]
([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)                         => [5,2,2]
([(0,3),(0,4),(3,5),(4,1),(4,5),(5,2)],6)                                     => [11]
([(0,4),(0,5),(4,3),(5,1),(5,2)],6)                                           => [6,4,3,3]
([(0,3),(0,4),(3,5),(4,1),(4,2),(4,5)],6)                                     => [6,5,4]
([(0,3),(0,4),(3,2),(3,5),(4,1),(4,5)],6)                                     => [8,4,2]
([(0,2),(0,3),(2,4),(2,5),(3,1),(3,4),(3,5)],6)                               => [5,4,2,2]
([(0,1),(0,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)                         => [4,2,2,2,2]
([(3,4),(4,5)],6)                                                             => [4,4,4,4,4,4,4,4]
([(2,3),(3,4),(3,5)],6)                                                       => [4,4,4,4,2,2,2,2]
([(1,5),(5,2),(5,3),(5,4)],6)                                                 => [4,4,2,2,2,2,2,2]
([(0,5),(5,1),(5,2),(5,3),(5,4)],6)                                           => [4,2,2,2,2,2,2,2]
([(2,3),(3,5),(5,4)],6)                                                       => [10,10]
([(1,4),(4,5),(5,2),(5,3)],6)                                                 => [10,2,2]
([(0,4),(4,5),(5,1),(5,2),(5,3)],6)                                           => [5,2,2,2]
([(3,5),(4,5)],6)                                                             => [6,6,6,6,2,2,2,2,2,2,2,2]
([(2,5),(3,5),(5,4)],6)                                                       => [4,4,4,4,2,2,2,2]
([(1,5),(2,5),(5,3),(5,4)],6)                                                 => [4,4,2,2,2,2]
([(0,5),(1,5),(5,2),(5,3),(5,4)],6)                                           => [4,2,2,2,2]
([(2,5),(3,5),(4,5)],6)                                                       => [6,6,2,2,2,2,2,2,2,2,2,2,2,2]
([(1,5),(2,5),(3,5),(5,4)],6)                                                 => [4,4,2,2,2,2,2,2]
([(0,5),(1,5),(2,5),(5,3),(5,4)],6)                                           => [4,2,2,2,2]
([(1,5),(2,5),(3,5),(4,5)],6)                                                 => [6,2,2,2,2,2,2,2,2,2,2,2,2,2,2]
([(0,5),(1,5),(2,5),(3,5),(5,4)],6)                                           => [4,2,2,2,2,2,2,2]
([(0,5),(1,5),(2,5),(3,5),(4,5)],6)                                           => [3,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2]
([(0,5),(1,5),(2,5),(3,4)],6)                                                 => [6,6,6,3,3,3]
([(0,5),(1,5),(2,5),(3,4),(5,3)],6)                                           => [5,2,2,2]
([(0,5),(1,5),(2,5),(3,4),(5,4)],6)                                           => [7,2,2,2,2,2,2]
([(0,5),(1,5),(2,5),(3,4),(3,5)],6)                                           => [6,6,6,5,3]
([(0,5),(1,5),(2,5),(3,4),(4,5)],6)                                           => [7,6,6,6]
([(1,5),(2,5),(3,4)],6)                                                       => [6,6,6,6,6]
([(1,5),(2,4),(3,4),(3,5)],6)                                                 => [8,8,6,2,2]
([(0,5),(1,4),(2,4),(2,5),(5,3)],6)                                           => [8,6,2]
([(0,4),(1,3),(2,3),(2,4),(3,5),(4,5)],6)                                     => [8,4,2]
([(1,5),(2,4),(2,5),(3,4),(3,5)],6)                                           => [10,6,2,2,2,2]
([(0,5),(1,4),(1,5),(2,4),(2,5),(4,3)],6)                                     => [8,3,2,2]
([(0,5),(1,3),(1,5),(2,3),(2,5),(3,4),(5,4)],6)                               => [5,4,2,2]
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)                                     => [6,2,2,2,2,2,2,2,2]
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(5,3)],6)                               => [7,2,2,2]
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)                         => [4,2,2,2,2]
([(0,5),(1,4),(1,5),(2,4),(2,5),(5,3)],6)                                     => [10,2,2]
([(1,5),(2,5),(3,4),(5,3)],6)                                                 => [10,2,2]
([(1,5),(2,4),(3,4),(4,5)],6)                                                 => [14,2,2,2,2]
([(0,5),(1,4),(2,4),(4,5),(5,3)],6)                                           => [8,2,2]
([(0,5),(1,5),(2,3),(5,4)],6)                                                 => [12,6]
([(0,5),(1,5),(4,2),(5,3),(5,4)],6)                                           => [8,2]
([(0,5),(1,5),(2,4),(5,3),(5,4)],6)                                           => [10,2,2]
([(1,5),(2,5),(3,4),(3,5)],6)                                                 => [10,6,6,6]
([(0,5),(1,5),(2,3),(2,5),(5,4)],6)                                           => [10,6]
([(0,5),(1,5),(2,3),(2,5),(3,4)],6)                                           => [8,4,4,3]
([(0,5),(1,5),(2,3),(2,5),(3,4),(5,4)],6)                                     => [6,5,4]
([(0,5),(1,5),(2,3),(2,4)],6)                                                 => [6,6,3,3,3,2,2]
([(0,5),(1,5),(4,2),(4,3),(5,4)],6)                                           => [5,2,2]
([(0,4),(1,4),(2,3),(2,5),(4,5)],6)                                           => [8,6,3]
([(0,3),(1,3),(2,4),(2,5),(3,4),(3,5)],6)                                     => [7,2,2,2]
([(0,5),(1,5),(2,3),(2,4),(2,5)],6)                                           => [6,6,5,3,2,2]
([(0,5),(1,2),(1,4),(3,5),(4,3)],6)                                           => [11,5]
([(0,3),(0,4),(1,5),(2,5),(4,1),(4,2)],6)                                     => [5,4,2,2]
([(0,3),(0,4),(1,5),(2,5),(3,2),(4,1)],6)                                     => [5,3,3]
([(0,5),(1,5),(2,3),(2,4),(4,5)],6)                                           => [10,6,2,2,2]
([(0,5),(1,3),(1,4),(2,5),(3,5),(4,2)],6)                                     => [15]
([(0,3),(0,4),(1,5),(2,5),(3,5),(4,1),(4,2)],6)                               => [8,2,2]
([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6)                                     => [7,6,2,2,2,2]
([(1,5),(2,5),(3,4),(4,5)],6)                                                 => [14,6,6]
([(0,5),(1,5),(2,3),(3,5),(5,4)],6)                                           => [8,6]
([(0,5),(1,5),(2,3),(3,4)],6)                                                 => [12,4,4]
([(0,5),(1,5),(3,2),(4,3),(5,4)],6)                                           => [6,2]
([(0,4),(1,4),(2,3),(3,5),(4,5)],6)                                           => [6,4,3,3]
([(0,5),(1,4),(3,5),(4,2),(4,3)],6)                                           => [8,4,2]
([(0,4),(2,5),(3,5),(4,1),(4,2),(4,3)],6)                                     => [8,2,2]
([(0,5),(1,5),(2,3),(3,4),(3,5)],6)                                           => [10,4,4]
([(0,5),(1,5),(2,3),(3,4),(4,5)],6)                                           => [5,4,4,4]
([(0,5),(1,4),(2,5),(3,5),(4,2),(4,3)],6)                                     => [5,4,2,2]
([(0,4),(1,5),(2,5),(3,5),(4,1),(4,2),(4,3)],6)                               => [5,2,2,2]
([(0,5),(1,5),(2,4),(3,4)],6)                                                 => [6,6,3,3,3,2,2]
([(0,5),(1,5),(2,4),(3,4),(3,5)],6)                                           => [8,6,3,2,2,2]
([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5)],6)                                     => [6,5,3,2,2,2,2]
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)                                     => [8,3,2,2,2,2,2]
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)                               => [5,3,2,2,2,2,2,2]
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)                         => [3,2,2,2,2,2,2,2,2]
([(0,5),(1,4),(2,4),(3,5),(4,3)],6)                                           => [5,4,2,2]
([(0,4),(1,4),(2,5),(3,5),(4,2),(4,3)],6)                                     => [5,2,2]
([(0,5),(1,5),(2,4),(3,4),(4,5)],6)                                           => [7,6,2,2,2,2]
([(2,5),(3,4)],6)                                                             => [6,6,6,6,6,6]
([(2,5),(3,4),(3,5)],6)                                                       => [10,10,6,6]
([(1,5),(2,3),(2,5),(3,4)],6)                                                 => [8,8,6]
([(0,5),(1,4),(1,5),(4,2),(4,3)],6)                                           => [8,6,3]
([(0,4),(1,2),(1,4),(2,3),(2,5),(4,5)],6)                                     => [6,4,3]
([(0,5),(1,2),(1,5),(2,3),(2,4),(5,3),(5,4)],6)                               => [5,4,2]
([(1,4),(2,3),(2,4),(3,5),(4,5)],6)                                           => [10,4,4]
([(0,4),(1,2),(1,4),(2,5),(4,5),(5,3)],6)                                     => [5,5]
([(0,5),(1,4),(1,5),(4,2),(5,3)],6)                                           => [10,4]
([(0,4),(1,2),(1,4),(2,5),(4,3),(4,5)],6)                                     => [8,4]
([(2,4),(2,5),(3,4),(3,5)],6)                                                 => [6,6,2,2,2,2,2,2,2,2]
([(1,4),(1,5),(2,4),(2,5),(5,3)],6)                                           => [14,2,2]
([(0,4),(0,5),(1,4),(1,5),(5,2),(5,3)],6)                                     => [7,2,2,2]
([(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)                                     => [4,4,2,2,2,2]
([(0,4),(0,5),(1,4),(1,5),(4,3),(5,2)],6)                                     => [4,3,3,2]
([(0,4),(0,5),(1,4),(1,5),(4,3),(5,2),(5,3)],6)                               => [5,4,2]
([(0,4),(0,5),(1,4),(1,5),(4,2),(4,3),(5,2),(5,3)],6)                         => [4,2,2,2]
([(0,4),(0,5),(1,4),(1,5),(2,3)],6)                                           => [6,6,3,3,3]
([(0,4),(0,5),(1,4),(1,5),(2,3),(5,2)],6)                                     => [5,4,2]
([(0,4),(0,5),(1,4),(1,5),(3,2),(4,3),(5,3)],6)                               => [5,2,2]
([(0,4),(0,5),(1,4),(1,5),(2,3),(4,2),(5,3)],6)                               => [8,2]
([(0,5),(1,3),(1,4),(2,3),(2,4),(4,5)],6)                                     => [10,2,2,2]
([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)                               => [7,2,2,2,2]
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,5)],6)                                     => [8,6,3,2]
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,5),(3,4)],6)                               => [10,2,2]
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5)],6)                               => [6,5,3,2,2]
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(3,5)],6)                               => [10,6]
([(0,4),(0,5),(1,4),(1,5),(2,3),(3,5)],6)                                     => [8,6,3]
([(0,4),(0,5),(1,4),(1,5),(2,3),(3,4),(3,5)],6)                               => [7,6,2]
([(1,5),(2,3),(2,5),(5,4)],6)                                                 => [10,10]
([(0,5),(1,2),(1,5),(5,3),(5,4)],6)                                           => [10,2,2]
([(1,5),(2,3),(2,4)],6)                                                       => [6,6,6,6,6]
([(1,5),(2,3),(2,4),(2,5)],6)                                                 => [10,6,6,6]
([(0,5),(1,3),(1,4),(1,5),(4,2)],6)                                           => [14,6]
([(0,4),(1,2),(1,3),(1,4),(3,5),(4,5)],6)                                     => [11,5]
([(0,4),(1,2),(1,3),(1,4),(2,5),(3,5)],6)                                     => [8,6,3]
([(0,4),(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6)                               => [6,5,4]
([(0,5),(1,2),(1,3),(1,5),(5,4)],6)                                           => [10,4,4]
([(0,5),(1,2),(1,3),(1,4)],6)                                                 => [6,6,6,3,3,3]
([(0,5),(1,2),(1,3),(1,4),(1,5)],6)                                           => [6,6,6,5,3]
([(0,2),(0,3),(0,5),(4,1),(5,4)],6)                                           => [5,4,4,4]
([(0,5),(1,2),(1,3),(1,4),(4,5)],6)                                           => [10,6,2,2,2]
([(0,2),(0,3),(0,4),(1,5),(3,5),(4,1)],6)                                     => [15]
([(0,5),(1,2),(1,3),(1,4),(3,5),(4,5)],6)                                     => [10,2,2,2,2,2]
([(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,1)],6)                               => [8,6]
([(0,5),(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6)                               => [7,2,2,2,2,2,2]
([(0,4),(1,2),(1,3),(1,5),(4,5)],6)                                           => [8,4,4,3]
([(0,3),(1,2),(1,4),(1,5),(3,4),(3,5)],6)                                     => [8,3,2,2]
([(0,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)                               => [7,2,2,2]
([(1,3),(1,5),(4,2),(5,4)],6)                                                 => [10,4,4]
([(0,3),(0,4),(4,5),(5,1),(5,2)],6)                                           => [5,4,2,2]
([(0,4),(0,5),(3,2),(4,3),(5,1)],6)                                           => [13]
([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6)                                     => [9,3]
([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)                               => [5,5]
([(0,3),(0,4),(2,5),(3,2),(4,1),(4,5)],6)                                     => [9,3]
([(0,2),(0,3),(1,4),(2,4),(2,5),(3,1),(3,5)],6)                               => [11]
([(1,5),(2,3),(2,4),(4,5)],6)                                                 => [10,10,2,2]
([(0,5),(1,2),(1,3),(3,5),(5,4)],6)                                           => [8,4,2]
([(1,3),(1,4),(2,5),(3,5),(4,2)],6)                                           => [8,8]
([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6)                                     => [9]
([(1,5),(2,3),(2,4),(3,5),(4,5)],6)                                           => [14,2,2,2,2]
([(0,5),(1,2),(1,3),(2,5),(3,5),(5,4)],6)                                     => [8,2,2]
([(0,5),(1,3),(1,4),(3,5),(4,2)],6)                                           => [11,3,3]
([(0,4),(1,2),(1,3),(2,5),(3,4),(3,5)],6)                                     => [13,2]
([(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6)                               => [10,2,2]
([(0,4),(1,2),(1,3),(2,5),(3,4),(4,5)],6)                                     => [11,2]
([(0,3),(0,4),(2,5),(3,5),(4,1),(4,2)],6)                                     => [11,2]
([(0,5),(1,3),(1,4),(3,5),(4,2),(4,5)],6)                                     => [11,5]
([(0,4),(1,3),(1,5),(5,2)],6)                                                 => [21]
([(0,3),(0,5),(4,2),(5,1),(5,4)],6)                                           => [15]
([(0,5),(1,3),(1,4),(4,2),(4,5)],6)                                           => [18]
([(0,4),(1,2),(1,3),(3,5),(4,5)],6)                                           => [11,3,3]
([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6)                                     => [6,4]
([(0,4),(1,2),(1,3),(2,5),(3,5)],6)                                           => [12,6]
([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6)                                     => [6,4,3,3]
([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)                                     => [6,2]
([(0,4),(1,2),(1,3),(2,5),(3,5),(5,4)],6)                                     => [5,4,2,2]
([(1,4),(1,5),(2,3),(2,5)],6)                                                 => [8,8,6,2,2]
([(1,4),(1,5),(2,3),(2,4),(2,5)],6)                                           => [10,6,2,2,2,2]
([(0,4),(0,5),(1,3),(1,4),(1,5),(5,2)],6)                                     => [9,7]
([(0,4),(0,5),(1,2),(1,4),(1,5),(4,3),(5,3)],6)                               => [10,2,2]
([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)                                     => [6,2,2,2,2,2,2,2,2]
([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(5,2)],6)                               => [7,6,2]
([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(4,2),(5,2)],6)                         => [7,2,2,2]
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6)                   => [4,2,2,2,2]
([(0,4),(0,5),(1,2),(1,4),(1,5),(2,3)],6)                                     => [8,6,3]
([(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(5,3)],6)                               => [7,5,2]
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6)                         => [5,4,2,2]
([(0,4),(0,5),(1,3),(1,5),(5,2)],6)                                           => [7,5,5]
([(1,4),(1,5),(2,3),(2,4),(3,5)],6)                                           => [10,10]
([(0,4),(0,5),(1,2),(1,4),(2,5),(4,3)],6)                                     => [6,4,3]
([(0,4),(0,5),(1,2),(1,4),(2,5),(5,3)],6)                                     => [7,5]
([(0,2),(0,5),(1,4),(1,5),(2,4),(4,3),(5,3)],6)                               => [11]
([(0,3),(0,5),(1,4),(1,5),(4,2)],6)                                           => [15,3]
([(0,2),(0,4),(1,3),(1,4),(3,5),(4,5)],6)                                     => [13,2]
([(0,4),(0,5),(1,2),(1,4),(2,3),(2,5)],6)                                     => [13,2]
([(0,2),(0,5),(1,4),(1,5),(2,3),(2,4),(5,3)],6)                               => [8,4]
([(0,3),(0,4),(1,2),(1,4),(2,5),(3,5)],6)                                     => [8,7]
([(0,3),(0,4),(1,2),(1,4),(2,5),(3,5),(4,5)],6)                               => [8,4,2]
([(0,4),(0,5),(1,2),(1,4),(2,3),(3,5)],6)                                     => [13]
([(0,4),(0,5),(1,2),(1,3)],6)                                                 => [6,6,3,3,3,2,2]
([(0,4),(0,5),(1,2),(1,3),(1,5)],6)                                           => [8,6,3,2,2,2]
([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5)],6)                                     => [6,5,3,2,2,2,2]
([(0,4),(0,5),(1,2),(1,3),(1,4),(3,5)],6)                                     => [18]
([(0,4),(0,5),(1,2),(1,3),(1,4),(2,5),(3,5)],6)                               => [10,6]
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5)],6)                                     => [8,3,2,2,2,2,2]
([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5)],6)                               => [5,3,2,2,2,2,2,2]
([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5)],6)                         => [3,2,2,2,2,2,2,2,2]
([(0,2),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3)],6)                               => [10,6]
([(0,3),(0,4),(1,2),(1,4),(1,5),(3,5)],6)                                     => [17]
([(0,2),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4)],6)                               => [10,2,2]
([(0,4),(0,5),(1,2),(1,3),(3,5)],6)                                           => [16,3]
([(0,4),(0,5),(1,2),(1,3),(3,4),(3,5)],6)                                     => [10,2,2,2]
([(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,1)],6)                               => [8,2]
([(0,2),(0,4),(2,5),(3,1),(3,5),(4,3)],6)                                     => [11]
([(0,4),(0,5),(1,2),(1,3),(2,5),(3,5)],6)                                     => [8,6,3]
([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6)                                     => [8,7]
([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4),(3,5)],6)                               => [7,5,2]
([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6)                         => [7,2,2,2]
([(0,3),(0,5),(1,2),(1,4),(2,5),(3,4)],6)                                     => [10,4]
([(1,4),(2,3),(2,5),(4,5)],6)                                                 => [8,8,6]
([(0,4),(1,3),(1,5),(4,5),(5,2)],6)                                           => [5,5,3]
([(1,4),(1,5),(2,3),(3,4),(3,5)],6)                                           => [14,2,2]
([(0,4),(0,5),(1,3),(3,4),(3,5),(5,2)],6)                                     => [11]
([(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)                               => [8,2]
([(0,3),(1,4),(1,5),(3,5),(4,2)],6)                                           => [7,4,4]
([(0,3),(1,2),(1,4),(2,5),(3,4),(4,5)],6)                                     => [9,3]
([(0,3),(1,2),(1,4),(2,5),(3,4),(3,5)],6)                                     => [6,4,3]
([(0,5),(1,3),(1,4),(5,2)],6)                                                 => [12,4,4]
([(0,2),(0,5),(3,4),(4,1),(5,3)],6)                                           => [11]
([(0,5),(4,2),(4,3),(5,1),(5,4)],6)                                           => [8,2,2]
([(0,4),(1,3),(1,5),(4,2),(4,5)],6)                                           => [8,6,2]
([(0,4),(0,5),(1,2),(2,3),(2,4),(2,5)],6)                                     => [10,2,2]
([(0,4),(0,5),(1,2),(2,3),(2,5),(3,4)],6)                                     => [7,5]
([(2,5),(3,4),(4,5)],6)                                                       => [14,14]
([(1,5),(2,3),(3,5),(5,4)],6)                                                 => [8,8]
([(0,5),(1,2),(2,5),(5,3),(5,4)],6)                                           => [8,2]
([(1,3),(2,4),(4,5)],6)                                                       => [12,12]
([(1,5),(4,3),(5,2),(5,4)],6)                                                 => [8,8]
([(1,5),(2,3),(3,4),(3,5)],6)                                                 => [10,10]
([(0,5),(1,4),(4,2),(4,5),(5,3)],6)                                           => [6,6]
([(0,4),(1,5),(5,2),(5,3)],6)                                                 => [12,6]
([(0,5),(4,3),(5,1),(5,2),(5,4)],6)                                           => [8,6]
([(0,5),(1,4),(4,2),(4,3),(4,5)],6)                                           => [10,6]
([(1,5),(3,4),(4,2),(5,3)],6)                                                 => [6,6]
([(0,4),(3,5),(4,3),(5,1),(5,2)],6)                                           => [6,2]
([(1,4),(2,3),(3,5),(4,5)],6)                                                 => [6,6,4,4]
([(0,4),(1,3),(3,5),(4,5),(5,2)],6)                                           => [5,3,3]
([(0,5),(1,4),(4,2),(5,3)],6)                                                 => [4,4,4,4]
([(0,5),(3,4),(4,2),(5,1),(5,3)],6)                                           => [6,4]
([(0,3),(1,4),(3,5),(4,2),(4,5)],6)                                           => [10,4]
([(0,3),(1,2),(2,4),(2,5),(3,4),(3,5)],6)                                     => [4,3,3,2]
([(1,5),(2,3),(3,4),(4,5)],6)                                                 => [10,4,4]
([(1,4),(2,5),(3,5),(4,2),(4,3)],6)                                           => [10,2,2]
([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)                                     => [6,2]
([(0,5),(1,4),(2,5),(4,2),(5,3)],6)                                           => [6,4]
([(0,5),(1,4),(2,3)],6)                                                       => [3,3,3,3,3,3,3,3,3]
([(0,5),(1,3),(2,4),(2,5)],6)                                                 => [15,3,3,3]
([(0,5),(1,4),(2,3),(2,4),(2,5)],6)                                           => [14,5,3]
([(0,5),(1,4),(1,5),(3,2),(4,3)],6)                                           => [9,5]
([(0,4),(1,2),(1,4),(2,3),(3,5),(4,5)],6)                                     => [9,3]
([(0,5),(1,4),(2,3),(2,4),(3,5)],6)                                           => [16,3]
([(0,4),(1,2),(1,4),(2,5),(3,5),(4,3)],6)                                     => [11]
([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6)                                     => [10,7]
([(0,5),(1,3),(1,5),(4,2),(5,4)],6)                                           => [7,5]
([(0,5),(1,4),(2,3),(2,4),(4,5)],6)                                           => [18]
([(0,4),(1,4),(1,5),(2,3),(2,5)],6)                                           => [11,7,3]
([(0,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)                                     => [8,6,3,2]
([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)                               => [6,5,3,2,2]
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4)],6)                                     => [5,5,5,3]
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5)],6)                               => [5,5,3,2,2]
([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)                         => [5,3,2,2,2,2]
([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)                   => [3,2,2,2,2,2,2]
([(0,4),(1,3),(1,5),(2,3),(2,4),(4,5)],6)                                     => [13,2]
([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5)],6)                                     => [7,5,5,3]
([(0,5),(1,4),(1,5),(2,3),(2,4),(3,5)],6)                                     => [18]
([(0,5),(1,4),(1,5),(2,3),(2,5)],6)                                           => [14,5,3]
([(0,5),(1,4),(1,5),(2,3),(2,5),(3,4)],6)                                     => [17]
([(0,4),(1,4),(1,5),(2,3),(3,5)],6)                                           => [15,3]
([(0,5),(1,4),(1,5),(2,3),(3,4),(3,5)],6)                                     => [9,7]
([(0,4),(1,3),(1,5),(2,5),(4,2)],6)                                           => [9,5]
([(0,4),(0,5),(1,2),(2,3),(3,4),(3,5)],6)                                     => [5,4,2]
([(0,3),(1,4),(1,5),(2,4),(2,5),(3,1),(3,2)],6)                               => [5,2,2]
([(0,4),(2,5),(3,1),(3,5),(4,2),(4,3)],6)                                     => [5,5]
([(0,5),(1,4),(2,3),(2,5),(4,5)],6)                                           => [14,6]
([(0,5),(1,3),(4,2),(5,4)],6)                                                 => [15]
([(0,5),(3,2),(4,1),(5,3),(5,4)],6)                                           => [5,3,3]
([(0,5),(1,4),(3,2),(4,3),(4,5)],6)                                           => [5,5,3]
([(0,5),(1,2),(2,3),(2,5),(3,4),(5,4)],6)                                     => [11]
([(0,4),(3,2),(4,5),(5,1),(5,3)],6)                                           => [9]
([(0,5),(1,3),(3,4),(4,2),(4,5)],6)                                           => [7,5]
([(0,5),(2,4),(3,2),(4,1),(5,3)],6)                                           => [7]
([(0,5),(1,3),(2,4),(4,5)],6)                                                 => [21]
([(0,5),(1,4),(2,3),(3,4),(3,5)],6)                                           => [7,5,5]
([(0,5),(1,3),(3,5),(4,2),(5,4)],6)                                           => [9]
([(0,5),(1,4),(2,3),(3,5),(5,4)],6)                                           => [15]
([(0,5),(1,4),(2,5),(3,2),(4,3)],6)                                           => [11]
([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)                                     => [6,2]
([(0,3),(1,4),(2,5),(3,5),(4,2)],6)                                           => [13]
([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6)                                     => [9]
([(0,5),(1,4),(2,3),(3,5),(4,5)],6)                                           => [7,6,6]
([],7)                                                                        => [2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2]
([(5,6)],7)                                                                   => [6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6]
([(4,5),(4,6)],7)                                                             => [6,6,6,6,6,6,6,6,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2]
([(3,4),(3,5),(3,6)],7)                                                       => [6,6,6,6,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2]
([(2,3),(2,4),(2,5),(2,6)],7)                                                 => [6,6,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2]
([(1,2),(1,3),(1,4),(1,5),(1,6)],7)                                           => [6,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2]
([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6)],7)                                     => [3,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2]
([(0,2),(0,3),(0,4),(0,5),(0,6),(6,1)],7)                                     => [7,6,6,6,6,6,6,6]
([(0,1),(0,2),(0,3),(0,4),(0,5),(4,6),(5,6)],7)                               => [7,6,6,6,2,2,2,2,2,2,2,2]
([(0,1),(0,2),(0,3),(0,4),(0,5),(3,6),(4,6),(5,6)],7)                         => [7,6,2,2,2,2,2,2,2,2,2,2,2,2]
([(0,1),(0,2),(0,3),(0,4),(0,5),(2,6),(3,6),(4,6),(5,6)],7)                   => [7,2,2,2,2,2,2,2,2,2,2,2,2,2,2]
([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)             => [4,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2]
([(1,3),(1,4),(1,5),(1,6),(6,2)],7)                                           => [14,6,6,6,6,6,6]
([(0,3),(0,4),(0,5),(0,6),(6,1),(6,2)],7)                                     => [7,6,6,6,2,2,2,2,2,2,2,2]
([(1,2),(1,3),(1,4),(1,5),(4,6),(5,6)],7)                                     => [14,6,6,2,2,2,2,2,2,2,2]
([(1,2),(1,3),(1,4),(1,5),(3,6),(4,6),(5,6)],7)                               => [14,2,2,2,2,2,2,2,2,2,2,2,2]
([(1,2),(1,3),(1,4),(1,5),(2,6),(3,6),(4,6),(5,6)],7)                         => [4,4,2,2,2,2,2,2,2,2,2,2,2,2,2,2]
([(0,2),(0,3),(0,4),(0,5),(2,6),(3,6),(4,6),(5,6),(6,1)],7)                   => [5,2,2,2,2,2,2,2]
([(0,2),(0,3),(0,4),(0,5),(2,6),(3,6),(4,6),(5,1)],7)                         => [6,6,6,4,3,3]
([(0,2),(0,3),(0,4),(0,5),(2,6),(3,6),(4,6),(5,1),(5,6)],7)                   => [6,6,6,5,4]
([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,6),(4,5),(6,5)],7)                   => [8,2,2,2,2,2,2]
([(0,2),(0,3),(0,4),(0,5),(3,6),(4,6),(5,6),(6,1)],7)                         => [5,4,2,2,2,2,2,2]
([(0,2),(0,3),(0,4),(0,5),(3,6),(4,6),(5,1)],7)                               => [7,6,6,6,6]
([(0,1),(0,2),(0,3),(0,4),(2,6),(3,5),(4,5),(4,6)],7)                         => [8,8,7,2,2]
([(0,1),(0,2),(0,3),(0,4),(2,6),(3,5),(3,6),(4,5),(4,6)],7)                   => [10,7,2,2,2,2]
([(0,1),(0,2),(0,3),(0,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)             => [7,2,2,2,2,2,2,2,2]
([(0,2),(0,3),(0,4),(0,5),(3,6),(4,6),(5,1),(5,6)],7)                         => [10,7,6,6]
([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,5)],7)                         => [6,6,4,3,3,2,2]
([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,5),(4,6)],7)                   => [8,6,4,2,2,2]
([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6)],7)             => [6,5,4,2,2,2,2]
([(0,1),(0,2),(0,3),(0,4),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7)             => [8,4,2,2,2,2,2]
([(0,1),(0,2),(0,3),(0,4),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)       => [5,4,2,2,2,2,2,2]
([(0,1),(0,2),(0,3),(0,4),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => [4,2,2,2,2,2,2,2,2]
([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,5),(5,6)],7)                   => [8,6,2,2,2,2]
([(0,1),(0,2),(0,3),(0,4),(2,6),(3,5),(4,5),(5,6)],7)                         => [15,2,2,2,2]
([(0,2),(0,3),(0,4),(0,5),(4,6),(5,6),(6,1)],7)                               => [5,4,4,4,2,2,2,2]
([(0,3),(0,4),(0,5),(0,6),(5,2),(6,1)],7)                                     => [7,6,6,6,6,6]
([(0,2),(0,3),(0,4),(0,5),(4,6),(5,1),(5,6)],7)                               => [10,10,7,6]
([(0,1),(0,2),(0,3),(0,4),(3,5),(3,6),(4,5),(4,6)],7)                         => [7,6,2,2,2,2,2,2,2,2]
([(2,4),(2,5),(2,6),(6,3)],7)                                                 => [14,14,6,6,6,6]
([(1,4),(1,5),(1,6),(6,2),(6,3)],7)                                           => [14,6,6,2,2,2,2,2,2,2,2]
([(0,4),(0,5),(0,6),(6,1),(6,2),(6,3)],7)                                     => [7,6,2,2,2,2,2,2,2,2,2,2,2,2]
([(2,3),(2,4),(2,5),(4,6),(5,6)],7)                                           => [14,14,2,2,2,2,2,2,2,2]
([(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7)                                     => [4,4,4,4,2,2,2,2,2,2,2,2,2,2,2,2]
([(1,2),(1,3),(1,4),(2,6),(3,6),(4,6),(6,5)],7)                               => [10,2,2,2,2,2,2]
([(0,3),(0,4),(0,5),(3,6),(4,6),(5,6),(6,1),(6,2)],7)                         => [5,2,2,2,2]
([(1,3),(1,4),(1,5),(3,6),(4,6),(5,2)],7)                                     => [6,6,6,6,4,4]
([(1,2),(1,3),(1,4),(2,6),(3,5),(4,5),(4,6)],7)                               => [8,8,4,4,2,2]
([(1,2),(1,3),(1,4),(2,6),(3,5),(3,6),(4,5),(4,6)],7)                         => [10,4,4,2,2,2,2]
([(1,2),(1,3),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)                   => [4,4,2,2,2,2,2,2,2,2]
([(0,2),(0,3),(0,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(6,1)],7)             => [8,2,2,2]
([(0,1),(0,2),(0,3),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(5,4),(6,4)],7)       => [5,2,2,2,2]
([(0,2),(0,3),(0,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,1)],7)                   => [9,3,2,2]
([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)             => [5,5,2,2]
([(0,2),(0,3),(0,4),(2,6),(3,5),(3,6),(4,5),(4,6),(6,1)],7)                   => [11,2,2]
([(0,2),(0,3),(0,4),(2,6),(3,5),(4,5),(4,6),(6,1)],7)                         => [9,6,2]
([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)                   => [8,5,2]
([(1,3),(1,4),(1,5),(3,6),(4,6),(5,2),(5,6)],7)                               => [10,6,6,4,4]
([(0,3),(0,4),(0,5),(3,6),(4,6),(5,1),(5,6),(6,2)],7)                         => [11,6]
([(0,3),(0,4),(0,5),(3,6),(4,6),(5,1),(5,2)],7)                               => [6,6,4,3,3,2,2]
([(0,3),(0,4),(0,5),(3,6),(4,6),(5,1),(5,2),(5,6)],7)                         => [6,6,5,4,2,2]
([(0,2),(0,3),(0,4),(2,5),(3,5),(4,1),(4,6),(5,6)],7)                         => [9,6,3]
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,5),(3,6),(4,5),(4,6)],7)                   => [8,2,2,2]
([(1,2),(1,3),(1,4),(2,6),(3,5),(4,5),(5,6)],7)                               => [8,8,2,2,2,2]
([(0,2),(0,3),(0,4),(2,6),(3,5),(4,5),(5,6),(6,1)],7)                         => [9,2,2]
([(0,3),(0,4),(0,5),(3,6),(4,6),(5,1),(6,2)],7)                               => [13,6]
([(0,2),(0,3),(0,4),(2,6),(3,6),(4,5),(6,1),(6,5)],7)                         => [11,2,2]
([(1,2),(1,3),(1,4),(3,6),(4,6),(6,5)],7)                                     => [10,4,4,2,2,2,2]
([(0,3),(0,4),(0,5),(4,6),(5,6),(6,1),(6,2)],7)                               => [5,4,2,2,2,2]
([(1,4),(1,5),(1,6),(5,3),(6,2)],7)                                           => [14,6,6,6,6]
([(1,3),(1,4),(1,5),(4,6),(5,2),(5,6)],7)                                     => [14,10,10]
([(1,2),(1,3),(1,4),(3,5),(3,6),(4,5),(4,6)],7)                               => [14,2,2,2,2,2,2,2,2]
([(0,2),(0,3),(0,4),(2,5),(2,6),(3,5),(3,6),(4,1)],7)                         => [6,6,4,3,3]
([(0,2),(0,3),(0,4),(2,5),(2,6),(3,5),(3,6),(4,1),(4,6)],7)                   => [8,6,4,2]
([(0,2),(0,3),(0,4),(2,5),(2,6),(3,5),(3,6),(4,1),(4,5),(4,6)],7)             => [6,5,4,2,2]
([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5)],7)             => [11,2,2]
([(0,1),(0,2),(0,3),(1,6),(2,4),(2,5),(3,4),(3,5),(5,6)],7)                   => [11,2,2,2]
([(0,1),(0,2),(0,3),(1,6),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7)             => [8,2,2,2,2]
([(0,2),(0,3),(0,4),(3,5),(3,6),(4,5),(4,6),(6,1)],7)                         => [15,2,2]
([(0,1),(0,2),(0,3),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7)                   => [5,4,2,2,2,2]
([(0,3),(0,4),(0,5),(4,6),(5,1),(5,6),(6,2)],7)                               => [11,10]
([(0,4),(0,5),(0,6),(5,3),(6,1),(6,2)],7)                                     => [7,6,6,6,6]
([(0,3),(0,4),(0,5),(4,6),(5,1),(5,2),(5,6)],7)                               => [10,7,6,6]
([(0,3),(0,4),(0,5),(4,2),(4,6),(5,1),(5,6)],7)                               => [8,8,7,2,2]
([(0,2),(0,3),(0,4),(3,5),(3,6),(4,1),(4,5),(4,6)],7)                         => [10,7,2,2,2,2]
([(0,1),(0,2),(0,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)                   => [7,2,2,2,2,2,2,2,2]
([(0,4),(0,5),(0,6),(4,3),(5,2),(6,1)],7)                                     => [4,3,3,3,3,3,3,3,3]
([(0,3),(0,4),(0,5),(3,6),(4,2),(5,1),(5,6)],7)                               => [15,4,3,3]
([(0,2),(0,3),(0,4),(2,6),(3,5),(4,1),(4,5),(4,6)],7)                         => [14,5,4]
([(0,2),(0,3),(0,4),(2,5),(3,5),(3,6),(4,1),(4,6)],7)                         => [11,7,4]
([(0,1),(0,2),(0,3),(1,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)                   => [8,6,4,2]
([(0,1),(0,2),(0,3),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)             => [6,5,4,2,2]
([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5)],7)                   => [5,5,5,4]
([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6)],7)             => [5,5,4,2,2]
([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)       => [5,4,2,2,2,2]
([(0,1),(0,2),(0,3),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => [4,2,2,2,2,2,2]
([(0,2),(0,3),(0,4),(2,6),(3,5),(3,6),(4,1),(4,5),(4,6)],7)                   => [7,5,5,4]
([(0,1),(0,2),(0,3),(1,5),(2,4),(2,6),(3,4),(3,5),(5,6)],7)                   => [14,2]
([(0,3),(0,4),(0,5),(3,6),(4,2),(4,6),(5,1),(5,6)],7)                         => [14,5,4]
([(0,2),(0,3),(0,4),(2,6),(3,5),(4,1),(4,5),(5,6)],7)                         => [19]
([(3,4),(3,5),(5,6)],7)                                                       => [14,14,14,14]
([(2,5),(2,6),(6,3),(6,4)],7)                                                 => [14,14,2,2,2,2,2,2,2,2]
([(1,5),(1,6),(6,2),(6,3),(6,4)],7)                                           => [14,2,2,2,2,2,2,2,2,2,2,2,2]
([(0,5),(0,6),(6,1),(6,2),(6,3),(6,4)],7)                                     => [7,2,2,2,2,2,2,2,2,2,2,2,2,2,2]
([(3,4),(3,5),(4,6),(5,6)],7)                                                 => [4,4,4,4,4,4,4,4,2,2,2,2,2,2,2,2]
([(2,3),(2,4),(3,6),(4,6),(6,5)],7)                                           => [10,10,2,2,2,2]
([(1,2),(1,3),(2,6),(3,6),(6,4),(6,5)],7)                                     => [10,2,2,2,2]
([(0,4),(0,5),(4,6),(5,6),(6,1),(6,2),(6,3)],7)                               => [5,2,2,2,2]
([(2,5),(2,6),(5,4),(6,3)],7)                                                 => [6,6,6,6,4,4,4,4]
([(2,3),(2,4),(3,6),(4,5),(4,6)],7)                                           => [10,10,4,4,4,4]
([(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7)                                     => [4,4,4,4,2,2,2,2,2,2,2,2]
([(1,3),(1,4),(3,5),(3,6),(4,5),(4,6),(6,2)],7)                               => [8,8,2,2]
([(0,3),(0,4),(3,5),(3,6),(4,5),(4,6),(6,1),(6,2)],7)                         => [8,2,2,2]
([(1,2),(1,3),(2,5),(2,6),(3,5),(3,6),(5,4),(6,4)],7)                         => [10,2,2,2,2]
([(0,2),(0,3),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6),(6,1)],7)                   => [6,2,2]
([(0,3),(0,4),(3,5),(3,6),(4,5),(4,6),(5,2),(6,1)],7)                         => [5,3,3,2]
([(0,2),(0,3),(2,4),(2,6),(3,4),(3,6),(4,5),(6,1),(6,5)],7)                   => [5,5,2]
([(0,1),(0,2),(1,5),(1,6),(2,5),(2,6),(5,3),(5,4),(6,3),(6,4)],7)             => [5,2,2,2]
([(1,3),(1,5),(3,6),(5,2),(5,6),(6,4)],7)                                     => [22]
([(0,4),(0,5),(4,6),(5,1),(5,6),(6,2),(6,3)],7)                               => [11,2,2]
([(1,5),(1,6),(5,4),(6,2),(6,3)],7)                                           => [6,6,6,6,4,4]
([(1,4),(1,5),(4,6),(5,2),(5,3),(5,6)],7)                                     => [10,6,6,4,4]
([(0,4),(0,5),(4,6),(5,1),(5,2),(5,6),(6,3)],7)                               => [11,4,4]
([(0,5),(0,6),(5,4),(6,1),(6,2),(6,3)],7)                                     => [6,6,6,4,3,3]
([(0,4),(0,5),(4,6),(5,1),(5,2),(5,3),(5,6)],7)                               => [6,6,6,5,4]
([(1,4),(1,5),(4,3),(4,6),(5,2),(5,6)],7)                                     => [8,8,4,4,2,2]
([(1,3),(1,4),(3,5),(3,6),(4,2),(4,5),(4,6)],7)                               => [10,4,4,2,2,2,2]
([(1,2),(1,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)                         => [4,4,2,2,2,2,2,2,2,2]
([(0,2),(0,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(6,1)],7)                   => [8,6,2]
([(0,1),(0,2),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(5,3),(6,3)],7)             => [8,2,2,2]
([(0,1),(0,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7)       => [5,2,2,2,2]
([(0,3),(0,4),(3,5),(3,6),(4,2),(4,5),(4,6),(6,1)],7)                         => [9,8]
([(0,2),(0,3),(2,4),(2,5),(3,1),(3,4),(3,5),(4,6),(5,6)],7)                   => [11,2,2]
([(0,4),(0,5),(4,2),(4,6),(5,1),(5,6),(6,3)],7)                               => [8,5,5]
([(0,5),(0,6),(5,3),(5,4),(6,1),(6,2)],7)                                     => [6,6,4,3,3,2,2]
([(0,4),(0,5),(4,3),(4,6),(5,1),(5,2),(5,6)],7)                               => [8,6,4,2,2,2]
([(0,3),(0,4),(3,5),(3,6),(4,1),(4,2),(4,5),(4,6)],7)                         => [6,5,4,2,2,2,2]
([(0,3),(0,4),(3,2),(3,5),(3,6),(4,1),(4,5),(4,6)],7)                         => [8,4,2,2,2,2,2]
([(0,2),(0,3),(2,4),(2,5),(2,6),(3,1),(3,4),(3,5),(3,6)],7)                   => [5,4,2,2,2,2,2,2]
([(0,1),(0,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6)],7)             => [4,2,2,2,2,2,2,2,2]
([(2,3),(2,4),(3,5),(4,6),(5,6)],7)                                           => [8,8,8,8]
([(1,3),(1,5),(2,6),(3,6),(5,2),(6,4)],7)                                     => [18]
([(0,4),(0,5),(1,6),(4,6),(5,1),(6,2),(6,3)],7)                               => [9,2]
([(4,5),(5,6)],7)                                                             => [4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4]
([(3,4),(4,5),(4,6)],7)                                                       => [4,4,4,4,4,4,4,4,2,2,2,2,2,2,2,2]
([(2,6),(6,3),(6,4),(6,5)],7)                                                 => [4,4,4,4,2,2,2,2,2,2,2,2,2,2,2,2]
([(1,6),(6,2),(6,3),(6,4),(6,5)],7)                                           => [4,4,2,2,2,2,2,2,2,2,2,2,2,2,2,2]
([(0,6),(6,1),(6,2),(6,3),(6,4),(6,5)],7)                                     => [4,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2]
([(3,4),(4,6),(6,5)],7)                                                       => [10,10,10,10]
([(2,5),(5,6),(6,3),(6,4)],7)                                                 => [10,10,2,2,2,2]
([(1,5),(5,6),(6,2),(6,3),(6,4)],7)                                           => [10,2,2,2,2,2,2]
([(0,5),(5,6),(6,1),(6,2),(6,3),(6,4)],7)                                     => [5,2,2,2,2,2,2,2]
([(4,6),(5,6)],7)                                                             => [6,6,6,6,6,6,6,6,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2]
([(3,6),(4,6),(6,5)],7)                                                       => [4,4,4,4,4,4,4,4,2,2,2,2,2,2,2,2]
([(2,6),(3,6),(6,4),(6,5)],7)                                                 => [4,4,4,4,2,2,2,2,2,2,2,2]
([(1,6),(2,6),(6,3),(6,4),(6,5)],7)                                           => [4,4,2,2,2,2,2,2,2,2]
([(0,6),(1,6),(6,2),(6,3),(6,4),(6,5)],7)                                     => [4,2,2,2,2,2,2,2,2]
([(3,6),(4,6),(5,6)],7)                                                       => [6,6,6,6,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2]
([(2,6),(3,6),(4,6),(6,5)],7)                                                 => [4,4,4,4,2,2,2,2,2,2,2,2,2,2,2,2]
([(1,6),(2,6),(3,6),(6,4),(6,5)],7)                                           => [4,4,2,2,2,2,2,2,2,2]
([(0,6),(1,6),(2,6),(6,3),(6,4),(6,5)],7)                                     => [4,2,2,2,2,2,2]
([(2,6),(3,6),(4,6),(5,6)],7)                                                 => [6,6,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2]
([(1,6),(2,6),(3,6),(4,6),(6,5)],7)                                           => [4,4,2,2,2,2,2,2,2,2,2,2,2,2,2,2]
([(0,6),(1,6),(2,6),(3,6),(6,4),(6,5)],7)                                     => [4,2,2,2,2,2,2,2,2]
([(1,6),(2,6),(3,6),(4,6),(5,6)],7)                                           => [6,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2]
([(0,6),(1,6),(2,6),(3,6),(4,6),(6,5)],7)                                     => [4,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2]
([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)                                     => [3,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2]
([(0,6),(1,6),(2,6),(3,6),(4,5)],7)                                           => [6,6,6,6,6,6,6,3,3,3]
([(0,6),(1,6),(2,6),(3,6),(4,5),(6,4)],7)                                     => [5,2,2,2,2,2,2,2]
([(0,6),(1,6),(2,6),(3,6),(4,5),(6,5)],7)                                     => [7,2,2,2,2,2,2,2,2,2,2,2,2,2,2]
([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6)],7)                                     => [6,6,6,6,6,6,6,5,3]
([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7)                                     => [7,6,6,6,6,6,6,6]
([(1,6),(2,6),(3,6),(4,5)],7)                                                 => [6,6,6,6,6,6,6,6,6]
([(1,6),(2,6),(3,6),(4,5),(6,4)],7)                                           => [10,2,2,2,2,2,2]
([(1,6),(2,6),(3,6),(4,5),(6,5)],7)                                           => [14,2,2,2,2,2,2,2,2,2,2,2,2]
([(0,6),(1,6),(2,6),(3,4),(6,5)],7)                                           => [12,6,6,6]
([(0,6),(1,6),(2,6),(4,5),(6,3),(6,4)],7)                                     => [8,2,2,2]
([(0,6),(1,6),(2,6),(3,5),(6,4),(6,5)],7)                                     => [10,2,2,2,2,2,2]
([(1,6),(2,6),(3,6),(4,5),(4,6)],7)                                           => [10,6,6,6,6,6,6,6]
([(0,6),(1,6),(2,6),(3,4),(3,6),(6,5)],7)                                     => [10,6,6,6]
([(0,6),(1,6),(2,6),(3,4),(3,6),(4,5)],7)                                     => [8,4,4,4,4,4,4,3]
([(0,6),(1,6),(2,6),(3,4),(3,6),(4,5),(6,5)],7)                               => [6,6,6,5,4]
([(0,6),(1,6),(2,6),(3,4),(3,5)],7)                                           => [6,6,6,6,3,3,3,2,2,2,2,2,2]
([(0,6),(1,6),(2,6),(3,4),(3,5),(6,3)],7)                                     => [5,2,2,2,2]
([(0,6),(1,6),(2,6),(3,4),(3,5),(6,5)],7)                                     => [8,6,6,6,3]
([(0,6),(1,6),(2,6),(3,4),(3,5),(6,4),(6,5)],7)                               => [7,2,2,2,2,2,2,2]
([(0,6),(1,6),(2,6),(3,4),(3,5),(3,6)],7)                                     => [6,6,6,6,5,3,2,2,2,2,2,2]
([(0,6),(1,6),(2,6),(3,4),(3,5),(5,6)],7)                                     => [10,6,6,6,2,2,2,2,2,2,2]
([(0,6),(1,6),(2,6),(3,4),(3,5),(4,6),(5,6)],7)                               => [7,6,6,6,2,2,2,2,2,2,2,2]
([(1,6),(2,6),(3,6),(4,5),(5,6)],7)                                           => [14,6,6,6,6,6,6]
([(0,6),(1,6),(2,6),(3,4),(4,6),(6,5)],7)                                     => [8,6,6,6]
([(0,6),(1,6),(2,6),(3,4),(4,5)],7)                                           => [12,4,4,4,4,4,4]
([(0,6),(1,6),(2,6),(3,5),(5,4),(6,3)],7)                                     => [6,2,2,2]
([(0,6),(1,6),(2,6),(3,5),(5,4),(6,5)],7)                                     => [8,2,2,2,2,2,2]
([(0,6),(1,6),(2,6),(3,4),(4,5),(6,5)],7)                                     => [6,6,6,4,3,3]
([(0,6),(1,6),(2,6),(3,4),(4,5),(4,6)],7)                                     => [10,4,4,4,4,4,4]
([(0,3),(1,6),(2,6),(3,5),(4,6),(5,4)],7)                                     => [11,10]
([(0,6),(1,4),(2,6),(3,6),(4,5),(5,2),(5,3)],7)                               => [11,2,2]
([(0,4),(1,6),(2,6),(3,6),(4,5),(5,1),(5,2),(5,3)],7)                         => [6,2,2,2]
([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7)                                     => [5,4,4,4,4,4,4,4]
([(0,6),(1,6),(2,6),(3,5),(4,5)],7)                                           => [6,6,6,6,3,3,3,2,2,2,2,2,2]
([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7)                                     => [8,6,6,3,2,2,2,2,2,2,2,2,2]
([(0,6),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7)                               => [8,6,3,2,2,2,2,2,2,2,2,2,2,2]
([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)                         => [6,5,3,2,2,2,2,2,2,2,2,2,2,2,2]
([(0,6),(1,5),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)                         => [8,3,2,2,2,2,2,2,2,2,2,2,2,2,2]
([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)                   => [5,3,2,2,2,2,2,2,2,2,2,2,2,2,2,2]
([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)             => [3,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2]
([(0,6),(1,6),(2,6),(3,5),(4,5),(6,4)],7)                                     => [5,4,2,2,2,2,2,2]
([(0,6),(1,6),(2,6),(3,5),(4,5),(6,3),(6,4)],7)                               => [5,2,2,2,2]
([(0,6),(1,6),(2,5),(3,5),(4,5),(5,6)],7)                                     => [7,6,2,2,2,2,2,2,2,2,2,2,2,2]
([(0,6),(1,6),(2,6),(3,5),(4,5),(4,6)],7)                                     => [8,6,6,6,3,2,2,2,2,2,2,2]
([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6)],7)                               => [6,6,6,5,3,2,2,2,2,2,2,2,2]
([(0,6),(1,6),(2,5),(3,5),(4,6),(5,4)],7)                                     => [5,4,4,4,2,2,2,2]
([(0,6),(1,5),(2,5),(3,6),(4,6),(5,3),(5,4)],7)                               => [5,4,2,2,2,2]
([(0,5),(1,5),(2,6),(3,6),(4,6),(5,2),(5,3),(5,4)],7)                         => [5,2,2,2,2]
([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7)                                     => [7,6,6,6,2,2,2,2,2,2,2,2]
([(2,6),(3,6),(4,5)],7)                                                       => [6,6,6,6,6,6,6,6,6,6]
([(2,6),(3,5),(4,5),(4,6)],7)                                                 => [8,8,8,8,6,6,2,2,2,2]
([(1,6),(2,5),(3,5),(3,6),(6,4)],7)                                           => [8,8,6,6,2,2]
([(0,6),(1,5),(2,5),(2,6),(6,3),(6,4)],7)                                     => [8,6,6,2]
([(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)                                     => [8,8,4,4,2,2]
([(0,5),(1,4),(2,4),(2,5),(4,6),(5,6),(6,3)],7)                               => [8,5,2]
([(0,6),(1,5),(2,5),(2,6),(5,3),(6,4)],7)                                     => [10,4,4,2]
([(0,6),(1,4),(2,4),(2,6),(4,5),(6,3),(6,5)],7)                               => [6,6,4,2]
([(0,6),(1,5),(2,5),(2,6),(5,3),(5,4),(6,3),(6,4)],7)                         => [8,4,2,2]
([(2,6),(3,5),(3,6),(4,5),(4,6)],7)                                           => [10,10,6,6,2,2,2,2,2,2,2,2]
([(1,6),(2,5),(2,6),(3,5),(3,6),(5,4)],7)                                     => [8,8,6,2,2,2,2]
([(0,6),(1,5),(1,6),(2,5),(2,6),(5,3),(5,4)],7)                               => [8,6,3,2,2]
([(0,6),(1,5),(1,6),(2,5),(2,6),(5,3),(5,4),(6,4)],7)                         => [6,4,3,2,2]
([(0,6),(1,3),(1,6),(2,3),(2,6),(3,4),(3,5),(6,4),(6,5)],7)                   => [5,4,2,2,2]
([(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)                               => [10,4,4,2,2,2,2]
([(0,6),(1,5),(1,6),(2,5),(2,6),(5,4),(6,3)],7)                               => [10,4,2,2]
([(0,6),(1,4),(1,6),(2,4),(2,6),(4,5),(6,3),(6,5)],7)                         => [8,4,2,2]
([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)                                     => [6,6,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2]
([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(6,4)],7)                               => [14,2,2,2,2,2,2]
([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(6,3),(6,4)],7)                         => [7,2,2,2,2,2]
([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(5,4),(6,4)],7)                         => [4,4,2,2,2,2,2,2,2,2]
([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(5,4),(6,3)],7)                         => [4,3,3,2,2,2]
([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(5,4),(6,3),(6,4)],7)                   => [5,4,2,2,2]
([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(5,3),(5,4),(6,3),(6,4)],7)             => [4,2,2,2,2,2]
([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4)],7)                               => [6,6,6,6,3,3,3]
([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(6,3)],7)                         => [5,4,2,2,2]
([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(4,3),(5,4),(6,4)],7)                   => [5,2,2,2,2]
([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(6,4)],7)                         => [10,2,2,2,2,2,2,2]
([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(5,4),(6,3)],7)                   => [8,2,2,2]
([(0,6),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7)                   => [7,2,2,2,2,2,2,2,2]
([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,6)],7)                         => [8,6,6,6,3,2]
([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,6),(5,4)],7)                   => [10,2,2,2,2,2,2]
([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6)],7)                   => [6,6,6,5,3,2,2]
([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(4,6)],7)                   => [10,6,6,6]
([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(4,6)],7)                         => [8,6,6,6,3]
([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(4,5),(4,6)],7)                   => [7,6,6,6,2]
([(1,6),(2,5),(2,6),(3,5),(3,6),(6,4)],7)                                     => [10,10,2,2,2,2]
([(0,6),(1,5),(1,6),(2,5),(2,6),(6,3),(6,4)],7)                               => [10,2,2,2,2]
([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4)],7)                                     => [15,6,6,3,3,3]
([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(5,3)],7)                               => [9,5,2,2]
([(0,6),(1,4),(1,6),(2,4),(2,6),(4,5),(5,3),(6,5)],7)                         => [5,5,2,2]
([(0,6),(1,4),(1,6),(2,4),(2,6),(3,5),(4,3),(6,5)],7)                         => [9,3,2,2]
([(0,5),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5)],7)                               => [16,3,2,2,2,2]
([(0,6),(1,4),(1,6),(2,4),(2,6),(3,5),(4,5),(6,3)],7)                         => [11,2,2]
([(0,6),(1,5),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7)                         => [10,7,2,2,2,2]
([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(6,3)],7)                               => [7,5,2,2]
([(0,6),(1,5),(2,4),(2,6),(3,4),(3,6),(6,5)],7)                               => [18,2,2,2,2]
([(0,5),(1,5),(1,6),(2,5),(2,6),(3,4),(3,6)],7)                               => [11,7,6,6,3]
([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(6,4)],7)                         => [13,2,2,2,2,2]
([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6)],7)                         => [7,6,6,5,5,3]
([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(4,6)],7)                         => [18,6,6]
([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,6)],7)                               => [14,6,6,5,3]
([(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5)],7)                         => [17,2,2,2,2]
([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,6),(4,5)],7)                         => [17,6,6]
([(0,5),(1,5),(1,6),(2,5),(2,6),(3,4),(4,6)],7)                               => [15,6,6,3]
([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(4,5),(4,6)],7)                         => [9,7,6,6]
([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(4,6)],7)                               => [14,6,6,6]
([(0,6),(1,5),(2,5),(2,6),(3,4)],7)                                           => [24,6,3,3,3]
([(0,6),(1,5),(2,4),(3,4),(3,5),(3,6)],7)                                     => [8,8,8,3,3,3,2]
([(0,6),(1,5),(2,5),(2,6),(3,4),(6,3)],7)                                     => [12,5,2]
([(0,6),(1,4),(2,5),(3,4),(3,5),(5,6)],7)                                     => [25,2,2]
([(0,5),(1,4),(2,4),(2,5),(3,6),(4,6),(5,3)],7)                               => [9,6,2]
([(0,6),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)                               => [8,8,7,2,2]
([(0,6),(1,5),(2,5),(2,6),(3,4),(3,6)],7)                                     => [17,10,6,3]
([(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5)],7)                               => [8,8,5,5,3,2]
([(0,5),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6)],7)                         => [8,7,5,3,2,2,2]
([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)                   => [7,5,5,3,2,2,2,2]
([(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6)],7)                         => [8,5,5,5,3,2,2]
([(0,6),(1,5),(1,6),(2,4),(3,4),(3,6),(4,5)],7)                               => [20,2,2,2]
([(0,6),(1,5),(2,5),(2,6),(3,4),(3,5),(3,6)],7)                               => [10,10,6,5,3]
([(0,6),(1,5),(2,5),(2,6),(3,4),(3,5),(4,6)],7)                               => [25,6]
([(0,6),(1,5),(2,5),(2,6),(3,4),(4,6)],7)                                     => [21,6,6]
([(0,6),(1,5),(2,5),(2,6),(3,4),(4,5),(4,6)],7)                               => [16,7,6]
([(2,6),(3,6),(4,5),(6,4)],7)                                                 => [10,10,2,2,2,2]
([(2,6),(3,5),(4,5),(5,6)],7)                                                 => [14,14,2,2,2,2,2,2,2,2]
([(1,6),(2,5),(3,5),(5,6),(6,4)],7)                                           => [8,8,2,2,2,2]
([(0,6),(1,5),(2,5),(5,6),(6,3),(6,4)],7)                                     => [8,2,2,2]
([(1,6),(2,6),(3,4),(6,5)],7)                                                 => [12,12,6,6]
([(1,6),(2,6),(4,5),(6,3),(6,4)],7)                                           => [8,8,2,2]
([(1,6),(2,6),(3,5),(6,4),(6,5)],7)                                           => [10,10,2,2,2,2]
([(0,6),(1,5),(2,5),(5,3),(5,6),(6,4)],7)                                     => [6,6,2,2]
([(0,6),(1,6),(2,3),(6,4),(6,5)],7)                                           => [12,6,6]
([(0,6),(1,6),(5,2),(6,3),(6,4),(6,5)],7)                                     => [8,6,2]
([(0,6),(1,6),(2,5),(6,3),(6,4),(6,5)],7)                                     => [10,6,2,2]
([(2,6),(3,6),(4,5),(4,6)],7)                                                 => [10,10,6,6,6,6,6,6]
([(1,6),(2,6),(3,4),(3,6),(6,5)],7)                                           => [10,10,6,6]
([(0,6),(1,6),(2,3),(2,6),(6,4),(6,5)],7)                                     => [10,6,2,2]
([(1,6),(2,6),(3,4),(3,6),(4,5)],7)                                           => [8,8,6,4,4,4,4]
([(1,6),(2,6),(3,4),(3,6),(4,5),(6,5)],7)                                     => [10,6,6,4,4]
([(0,6),(1,6),(2,3),(2,6),(3,5),(6,4)],7)                                     => [10,4,4,4]
([(0,6),(1,6),(2,4),(2,6),(4,5),(6,3),(6,5)],7)                               => [8,6,4]
([(0,6),(1,6),(2,3),(2,6),(3,4),(3,5)],7)                                     => [8,6,4,4,3,2,2]
([(0,6),(1,6),(2,3),(2,6),(3,4),(3,5),(6,5)],7)                               => [6,4,4,4,3]
([(0,6),(1,6),(2,3),(2,6),(3,4),(3,5),(6,4),(6,5)],7)                         => [6,5,4,2]
([(0,6),(1,6),(2,3),(2,6),(3,5),(5,4)],7)                                     => [10,9,5]
([(0,6),(1,6),(2,3),(2,6),(3,5),(5,4),(6,5)],7)                               => [6,5,5]
([(0,6),(1,6),(2,3),(2,6),(3,4),(4,5),(6,5)],7)                               => [9,4,4,3]
([(1,6),(2,6),(3,4),(3,5)],7)                                                 => [6,6,6,6,6,6,6,2,2,2,2]
([(1,6),(2,6),(3,4),(3,5),(6,3)],7)                                           => [10,2,2,2,2]
([(1,5),(2,5),(3,4),(3,6),(5,6)],7)                                           => [8,8,6,6,6]
([(1,4),(2,4),(3,5),(3,6),(4,5),(4,6)],7)                                     => [14,2,2,2,2,2,2]
([(0,5),(0,6),(1,4),(2,4),(4,5),(4,6),(6,3)],7)                               => [11,2,2]
([(0,5),(1,5),(2,4),(2,6),(5,6),(6,3)],7)                                     => [6,5,5,3]
([(0,6),(1,6),(2,3),(2,4),(6,5)],7)                                           => [12,6,4,4,2,2]
([(0,6),(1,6),(5,2),(5,3),(6,4),(6,5)],7)                                     => [8,2,2,2]
([(0,6),(1,6),(2,4),(2,5),(6,3),(6,5)],7)                                     => [8,6,6,2]
([(0,6),(1,6),(2,4),(2,5),(6,3),(6,4),(6,5)],7)                               => [10,2,2,2,2]
([(1,6),(2,6),(3,4),(3,5),(3,6)],7)                                           => [10,6,6,6,6,6,2,2,2,2]
([(0,6),(1,6),(2,3),(2,4),(2,6),(6,5)],7)                                     => [10,6,4,4,2,2]
([(0,6),(1,6),(2,3),(2,4),(2,6),(4,5)],7)                                     => [14,14,6]
([(0,6),(1,6),(2,3),(2,4),(2,6),(4,5),(6,5)],7)                               => [11,6,5,2,2]
([(0,6),(1,6),(2,3),(2,4),(2,6),(3,5),(4,5)],7)                               => [8,6,4,4,3,2,2]
([(0,5),(1,5),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7)                         => [6,6,5,4,2,2]
([(0,6),(1,6),(2,3),(2,4),(2,5)],7)                                           => [6,6,6,6,3,3,3,2,2,2,2,2,2]
([(0,6),(1,6),(5,2),(5,3),(5,4),(6,5)],7)                                     => [5,2,2,2,2]
([(0,5),(1,5),(2,3),(2,4),(2,6),(5,6)],7)                                     => [8,6,4,4,3,2,2]
([(0,4),(1,4),(2,3),(2,5),(2,6),(4,5),(4,6)],7)                               => [8,6,3,2,2]
([(0,6),(1,6),(2,3),(2,4),(2,5),(6,3),(6,4),(6,5)],7)                         => [7,2,2,2,2,2]
([(0,6),(1,6),(2,3),(2,4),(2,5),(2,6)],7)                                     => [6,6,6,6,5,3,2,2,2,2,2,2]
([(0,6),(1,2),(1,3),(1,5),(4,6),(5,4)],7)                                     => [14,11,5]
([(0,3),(0,4),(0,5),(1,6),(2,6),(5,1),(5,2)],7)                               => [5,4,4,4,2,2,2,2]
([(0,3),(0,4),(0,5),(1,6),(2,6),(4,2),(5,1)],7)                               => [6,6,5,4]
([(0,6),(1,6),(2,3),(2,4),(2,5),(5,6)],7)                                     => [10,6,6,2,2,2,2,2,2,2,2,2]
([(0,6),(1,2),(1,4),(1,5),(3,6),(4,6),(5,3)],7)                               => [22,6]
([(0,3),(0,4),(0,5),(1,6),(2,6),(4,6),(5,1),(5,2)],7)                         => [15,2,2,2,2]
([(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,2),(5,1)],7)                         => [8,6,6]
([(0,6),(1,6),(2,3),(2,4),(2,5),(4,6),(5,6)],7)                               => [10,6,2,2,2,2,2,2,2,2,2,2,2]
([(0,6),(1,3),(1,4),(1,5),(2,6),(3,6),(4,6),(5,2)],7)                         => [15,6,6]
([(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,1),(5,2)],7)                   => [8,6,2,2,2,2]
([(0,6),(1,6),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7)                         => [7,6,2,2,2,2,2,2,2,2,2,2,2,2]
([(1,6),(2,6),(3,4),(3,5),(5,6)],7)                                           => [10,10,6,6,2,2,2,2,2,2]
([(0,6),(1,6),(2,3),(2,4),(4,6),(6,5)],7)                                     => [8,6,4,2,2,2]
([(1,6),(2,6),(3,4),(3,5),(4,6),(5,6)],7)                                     => [14,6,6,2,2,2,2,2,2,2,2]
([(0,6),(1,6),(2,3),(2,4),(3,6),(4,6),(6,5)],7)                               => [8,6,2,2,2,2]
([(0,6),(1,6),(2,3),(2,4),(4,5)],7)                                           => [21,14]
([(0,6),(1,6),(4,3),(5,2),(5,4),(6,5)],7)                                     => [9,2]
([(0,5),(1,5),(2,3),(2,6),(3,4),(5,6)],7)                                     => [7,4,4,4,4]
([(0,4),(1,4),(2,3),(2,5),(3,6),(4,5),(4,6)],7)                               => [6,6,4,3]
([(0,4),(1,4),(2,3),(2,5),(3,6),(4,5),(5,6)],7)                               => [9,6,3]
([(0,6),(1,6),(2,4),(2,5),(4,3),(5,3),(6,4),(6,5)],7)                         => [8,2,2,2]
([(0,5),(1,5),(2,3),(2,4),(4,6),(5,6)],7)                                     => [11,6,3,3,2,2]
([(0,6),(1,3),(1,5),(4,6),(5,2),(5,4)],7)                                     => [22,2,2]
([(0,4),(0,5),(2,6),(3,6),(5,1),(5,2),(5,3)],7)                               => [15,2,2,2,2]
([(0,6),(1,6),(2,3),(2,4),(4,5),(4,6)],7)                                     => [18,14]
([(0,6),(1,4),(1,5),(3,6),(4,2),(5,3)],7)                                     => [19,4]
([(0,6),(1,3),(1,4),(2,6),(3,5),(4,2),(6,5)],7)                               => [11,6]
([(0,6),(1,4),(1,5),(3,6),(4,3),(5,2),(5,6)],7)                               => [12,6,4]
([(0,4),(0,5),(2,6),(3,6),(4,1),(4,6),(5,2),(5,3)],7)                         => [9,6,3]
([(0,3),(0,4),(1,6),(2,6),(3,5),(3,6),(4,1),(4,2),(4,5)],7)                   => [11,6]
([(0,6),(1,3),(1,4),(2,6),(3,5),(3,6),(4,2),(4,5)],7)                         => [16,4]
([(0,4),(0,5),(2,6),(3,6),(4,3),(5,1),(5,2)],7)                               => [12,3,3]
([(0,3),(0,4),(1,5),(2,5),(3,2),(3,6),(4,1),(4,6)],7)                         => [8,8]
([(0,3),(0,4),(1,6),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6)],7)                   => [8,5,2]
([(0,4),(0,5),(2,6),(3,6),(4,1),(5,2),(5,3)],7)                               => [13,6]
([(0,3),(0,4),(1,5),(2,5),(3,6),(4,1),(4,2),(5,6)],7)                         => [6,4,2,2]
([(0,3),(0,4),(1,5),(2,5),(3,6),(4,1),(4,2),(4,6)],7)                         => [9,6,3]
([(0,3),(0,4),(1,6),(2,6),(3,5),(4,1),(4,2),(4,5),(5,6)],7)                   => [6,5,5]
([(0,6),(1,3),(1,4),(2,6),(3,5),(4,2),(4,5)],7)                               => [14,4,3]
([(0,6),(1,3),(1,4),(2,6),(3,5),(4,2),(4,5),(5,6)],7)                         => [10,5,4]
([(0,3),(0,4),(1,5),(2,5),(3,6),(4,2),(4,6),(6,1)],7)                         => [12]
([(0,6),(1,6),(2,3),(2,4),(3,5),(4,6)],7)                                     => [14,11,3,3]
([(0,6),(1,6),(2,3),(2,4),(3,6),(4,5),(6,5)],7)                               => [11,6,2,2,2]
([(0,6),(1,4),(1,5),(3,6),(4,6),(5,2),(5,3)],7)                               => [18,2,2,2]
([(0,4),(0,5),(2,6),(3,6),(4,6),(5,1),(5,2),(5,3)],7)                         => [11,2,2,2,2,2]
([(0,6),(1,6),(2,3),(2,4),(3,6),(4,5),(4,6)],7)                               => [14,11,5]
([(0,6),(1,6),(2,3),(2,4),(3,5),(4,6),(5,6)],7)                               => [15,14]
([(0,6),(1,4),(1,5),(2,6),(3,6),(4,6),(5,2),(5,3)],7)                         => [15,2,2,2,2]
([(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,1),(5,2),(5,3)],7)                   => [8,2,2,2,2,2,2]
([(0,5),(1,5),(2,3),(2,4),(3,6),(4,6)],7)                                     => [12,6,4,4,2,2]
([(0,6),(1,6),(2,5),(3,5),(4,2),(4,3),(6,4)],7)                               => [6,2,2]
([(0,5),(1,5),(2,3),(2,4),(3,6),(4,6),(5,6)],7)                               => [6,6,4,3,3,2,2]
([(0,6),(1,6),(2,3),(2,4),(3,5),(4,5),(4,6)],7)                               => [13,4,4,2,2,2]
([(0,6),(1,6),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7)                         => [10,4,4,2,2,2,2]
([(0,5),(1,2),(1,3),(2,6),(3,6),(4,5),(6,4)],7)                               => [11,2,2]
([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)                         => [6,2,2]
([(0,6),(1,6),(2,3),(2,4),(3,5),(4,5),(5,6)],7)                               => [5,4,4,4,2,2,2,2]
([(0,6),(1,6),(2,3),(2,4),(4,5),(5,6)],7)                                     => [14,11,5]
([(0,6),(1,2),(1,5),(3,6),(4,6),(5,3),(5,4)],7)                               => [11,5,2,2,2,2]
([(0,4),(0,5),(1,6),(2,6),(3,6),(5,1),(5,2),(5,3)],7)                         => [5,4,2,2,2,2,2,2]
([(0,6),(1,4),(1,5),(2,6),(3,6),(4,3),(5,2)],7)                               => [6,6,5,4]
([(0,4),(0,5),(1,6),(2,6),(3,6),(4,3),(5,1),(5,2)],7)                         => [6,5,3,3]
([(2,6),(3,6),(4,5),(5,6)],7)                                                 => [14,14,6,6,6,6]
([(1,6),(2,6),(3,4),(4,6),(6,5)],7)                                           => [8,8,6,6]
([(0,6),(1,6),(2,3),(3,6),(6,4),(6,5)],7)                                     => [8,6,2]
([(1,6),(2,6),(3,4),(4,5)],7)                                                 => [12,12,4,4,4,4]
([(1,6),(2,6),(3,5),(5,4),(6,3)],7)                                           => [6,6,2,2]
([(1,5),(2,5),(3,4),(4,6),(5,6)],7)                                           => [6,6,6,6,4,4]
([(0,5),(1,5),(2,3),(3,6),(5,6),(6,4)],7)                                     => [6,5,3,3]
([(0,6),(1,6),(2,3),(3,5),(6,4)],7)                                           => [4,4,4,4,4,4]
([(0,6),(1,6),(4,2),(5,4),(6,3),(6,5)],7)                                     => [6,4,2]
([(0,5),(1,5),(2,3),(3,6),(5,4),(5,6)],7)                                     => [10,6,4]
([(1,6),(2,6),(3,4),(4,5),(4,6)],7)                                           => [10,10,4,4,4,4]
([(0,6),(1,6),(2,3),(3,5),(3,6),(6,4)],7)                                     => [6,6,4,4]
([(0,3),(1,6),(2,6),(3,5),(3,6),(5,4)],7)                                     => [10,5,5,3]
([(0,6),(1,6),(2,3),(3,4),(3,6),(4,5),(6,5)],7)                               => [11,4,4]
([(0,3),(1,6),(2,6),(3,4),(3,5)],7)                                           => [12,6,4,4,2,2]
([(0,6),(1,6),(4,5),(5,2),(5,3),(6,4)],7)                                     => [6,2,2]
([(0,5),(1,5),(2,3),(3,4),(3,6),(5,6)],7)                                     => [10,4,4,4]
([(0,4),(1,4),(2,3),(3,5),(3,6),(4,5),(4,6)],7)                               => [6,4,3,3,2]
([(0,6),(1,5),(4,6),(5,2),(5,3),(5,4)],7)                                     => [8,6,4,2,2,2]
([(0,5),(3,6),(4,6),(5,1),(5,2),(5,3),(5,4)],7)                               => [8,6,2,2,2,2]
([(0,3),(1,6),(2,6),(3,4),(3,5),(3,6)],7)                                     => [10,6,4,4,2,2]
([(0,3),(1,6),(2,6),(3,4),(3,5),(5,6)],7)                                     => [8,4,4,4,2,2,2]
([(0,6),(1,5),(3,6),(4,6),(5,2),(5,3),(5,4)],7)                               => [8,4,2,2,2,2,2]
([(0,5),(2,6),(3,6),(4,6),(5,1),(5,2),(5,3),(5,4)],7)                         => [8,2,2,2,2,2,2]
([(0,3),(1,6),(2,6),(3,4),(3,5),(4,6),(5,6)],7)                               => [5,4,4,4,2,2,2,2]
([(0,6),(1,5),(2,6),(3,6),(4,6),(5,2),(5,3),(5,4)],7)                         => [5,4,2,2,2,2,2,2]
([(0,5),(1,6),(2,6),(3,6),(4,6),(5,1),(5,2),(5,3),(5,4)],7)                   => [5,2,2,2,2,2,2,2]
([(1,3),(2,6),(3,5),(4,6),(5,4)],7)                                           => [22]
([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7)                                     => [12]
([(1,4),(2,6),(3,6),(4,5),(5,2),(5,3)],7)                                     => [6,6,2,2]
([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)                               => [7,2]
([(1,6),(2,6),(3,4),(4,5),(5,6)],7)                                           => [10,4,4,4,4,4,4]
([(0,6),(1,6),(2,3),(3,5),(5,6),(6,4)],7)                                     => [6,4,4,4]
([(0,3),(1,6),(2,6),(3,5),(5,4)],7)                                           => [15,10]
([(0,6),(1,6),(3,4),(4,2),(5,3),(6,5)],7)                                     => [7,2]
([(0,5),(1,5),(2,3),(3,4),(4,6),(5,6)],7)                                     => [13,4,4]
([(0,6),(1,4),(3,6),(4,5),(5,2),(5,3)],7)                                     => [14,2]
([(0,4),(2,6),(3,6),(4,5),(5,1),(5,2),(5,3)],7)                               => [9,2,2]
([(0,3),(1,6),(2,6),(3,5),(5,4),(5,6)],7)                                     => [10,7,5]
([(1,6),(2,6),(3,5),(4,5)],7)                                                 => [6,6,6,6,6,6,6,2,2,2,2]
([(1,6),(2,6),(3,5),(4,5),(4,6)],7)                                           => [8,8,6,6,6,2,2,2,2,2,2]
([(0,6),(1,6),(2,5),(3,5),(3,6),(5,4)],7)                                     => [8,6,4,4,2,2,2]
([(0,6),(1,6),(2,4),(3,4),(3,6),(4,5),(6,5)],7)                               => [8,6,4,2,2,2]
([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6)],7)                                     => [10,6,6,6,2,2,2,2,2,2,2,2]
([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(5,4)],7)                               => [8,4,4,3,2,2,2,2]
([(0,6),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)                         => [6,5,4,2,2,2,2]
([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(6,4)],7)                               => [10,6,2,2,2,2]
([(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7)                                     => [8,8,6,2,2,2,2,2,2,2,2,2,2]
([(0,6),(1,5),(2,5),(2,6),(3,5),(3,6),(6,4)],7)                               => [8,6,2,2,2,2,2]
([(0,6),(1,5),(2,5),(2,6),(3,5),(3,6),(5,4),(6,4)],7)                         => [8,4,2,2,2,2,2]
([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)                               => [10,6,2,2,2,2,2,2,2,2,2,2,2,2]
([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(5,4)],7)                         => [8,3,2,2,2,2,2,2]
([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(5,4),(6,4)],7)                   => [5,4,2,2,2,2,2,2]
([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(6,4)],7)                         => [10,2,2,2,2,2,2]
([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)                         => [6,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2]
([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(6,4)],7)                   => [7,2,2,2,2,2,2,2]
([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(5,4),(6,4)],7)             => [4,2,2,2,2,2,2,2,2]
([(0,6),(1,6),(2,5),(3,5),(3,6),(6,4)],7)                                     => [8,6,6,2,2,2]
([(1,6),(2,5),(3,5),(4,6),(5,4)],7)                                           => [10,4,4,2,2,2,2]
([(1,5),(2,5),(3,6),(4,6),(5,3),(5,4)],7)                                     => [10,2,2,2,2]
([(0,6),(1,5),(2,5),(4,6),(5,4),(6,3)],7)                                     => [6,4,2,2]
([(0,6),(1,6),(2,5),(3,5),(5,4),(6,2),(6,3)],7)                               => [6,2,2]
([(1,6),(2,6),(3,5),(4,5),(5,6)],7)                                           => [14,6,6,2,2,2,2,2,2,2,2]
([(0,6),(1,6),(2,5),(3,5),(5,6),(6,4)],7)                                     => [8,6,2,2,2,2]
([(0,6),(1,6),(2,5),(3,5),(6,4)],7)                                           => [12,6,4,4,2,2]
([(0,6),(1,5),(2,5),(4,6),(5,3),(5,4)],7)                                     => [8,4,2,2,2]
([(0,6),(1,6),(3,5),(4,5),(6,2),(6,3),(6,4)],7)                               => [8,2,2,2]
([(0,6),(1,6),(2,5),(3,5),(5,4),(5,6)],7)                                     => [10,4,4,2,2,2,2]
([(0,5),(1,5),(2,4),(3,4),(4,6),(5,6)],7)                                     => [6,6,4,3,3,2,2]
([(0,6),(1,6),(2,5),(3,4)],7)                                                 => [6,6,6,3,3,3,3,3,3,3,3,3]
([(0,6),(1,6),(2,3),(4,5),(6,4)],7)                                           => [15,6]
([(0,6),(1,6),(4,3),(5,2),(6,4),(6,5)],7)                                     => [5,3,3,2]
([(0,6),(1,6),(2,5),(3,4),(6,3),(6,5)],7)                                     => [5,5,3,2,2]
([(0,6),(1,5),(2,5),(3,4),(5,6)],7)                                           => [21,6,6]
([(0,4),(1,4),(2,6),(3,5),(4,5),(4,6)],7)                                     => [7,5,5,2,2,2,2]
([(0,6),(1,5),(2,5),(3,4),(5,6),(6,3)],7)                                     => [9,2,2]
([(0,4),(1,4),(2,5),(3,6),(4,6),(6,5)],7)                                     => [15,2,2,2,2]
([(0,6),(1,6),(2,5),(3,4),(3,6)],7)                                           => [15,6,6,6,3,3,3]
([(0,6),(1,6),(2,3),(2,6),(4,5),(6,4)],7)                                     => [7,6,5]
([(0,6),(1,6),(2,5),(3,4),(3,6),(6,5)],7)                                     => [18,6,6]
([(0,6),(1,6),(2,5),(3,4),(3,6),(4,5)],7)                                     => [16,14,3]
([(0,6),(1,6),(2,3),(2,6),(3,5),(4,5),(6,4)],7)                               => [11,6]
([(0,6),(1,5),(2,5),(3,4),(3,5),(4,6),(5,6)],7)                               => [10,7,6,6]
([(0,6),(1,6),(2,5),(2,6),(3,4),(3,6)],7)                                     => [14,6,6,6,5,3]
([(0,6),(1,6),(2,5),(2,6),(3,4),(3,6),(4,5)],7)                               => [17,14]
([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5)],7)                                     => [11,10,7,6,3]
([(0,6),(1,6),(2,4),(2,6),(3,4),(3,5),(6,5)],7)                               => [13,6,2,2,2]
([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6)],7)                               => [10,7,6,5,5,3]
([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(4,6)],7)                               => [18,10,6]
([(0,6),(1,6),(2,5),(3,4),(3,6),(5,6)],7)                                     => [14,6,6,6,6]
([(0,6),(1,6),(2,5),(2,6),(3,4),(4,5)],7)                                     => [15,14,3]
([(0,6),(1,6),(2,5),(2,6),(3,4),(4,5),(4,6)],7)                               => [14,9,7]
([(0,5),(1,5),(2,6),(3,4),(3,6)],7)                                           => [15,10,6,3,3,3]
([(0,5),(1,4),(2,4),(2,6),(3,5),(3,6)],7)                                     => [14,10,5,3,2]
([(0,6),(1,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)                               => [12,8,5,3,2,2]
([(0,6),(1,5),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)                         => [14,5,3,2,2,2,2]
([(0,5),(1,4),(1,5),(2,4),(2,6),(3,6),(5,3)],7)                               => [16,2]
([(0,6),(1,5),(2,4),(2,6),(3,4),(3,5),(5,6)],7)                               => [16,8,2,2]
([(0,6),(1,5),(2,5),(3,4),(3,6),(5,3)],7)                                     => [7,5,2,2]
([(0,4),(1,5),(2,5),(3,4),(3,6),(5,6)],7)                                     => [15,6,3,2,2]
([(0,6),(1,5),(1,6),(2,4),(3,4),(4,5),(4,6)],7)                               => [9,7,2,2,2,2]
([(0,5),(1,5),(2,3),(2,6),(4,6),(5,4)],7)                                     => [9,6,5]
([(0,6),(1,6),(3,5),(4,2),(4,5),(6,3),(6,4)],7)                               => [5,5,2]
([(0,5),(1,5),(2,4),(2,6),(3,6),(5,3),(5,4)],7)                               => [7,5,2,2]
([(0,6),(1,5),(2,5),(3,4),(3,6),(5,6)],7)                                     => [14,6,6,6]
([(0,6),(1,6),(2,5),(3,4),(3,5),(3,6)],7)                                     => [14,10,6,5,3]
([(0,6),(1,6),(2,5),(3,4),(3,5),(4,6)],7)                                     => [16,10,6,3]
([(0,6),(1,5),(2,3),(2,5),(3,6),(4,6),(5,4)],7)                               => [11,10]
([(0,5),(1,2),(1,5),(2,6),(3,6),(4,6),(5,3),(5,4)],7)                         => [11,2,2]
([(0,6),(1,6),(2,5),(3,4),(3,5),(4,6),(5,6)],7)                               => [10,10,7,6]
([(0,4),(1,4),(2,5),(2,6),(3,5),(3,6)],7)                                     => [6,6,6,3,3,3,2,2,2,2]
([(0,5),(1,4),(1,6),(2,4),(2,6),(3,5),(3,6)],7)                               => [11,7,6,3,2,2]
([(0,5),(0,6),(1,5),(1,6),(2,4),(3,4),(3,5),(3,6)],7)                         => [8,6,6,3,2,2,2]
([(0,6),(1,4),(1,5),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)                   => [8,6,3,2,2,2,2,2]
([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)             => [6,5,3,2,2,2,2,2,2]
([(0,5),(0,6),(1,5),(1,6),(2,4),(3,4),(3,5),(4,6)],7)                         => [13,6,2,2,2]
([(0,5),(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,6)],7)                         => [8,6,6,3,2,2,2]
([(0,5),(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5)],7)                   => [10,6,2,2,2,2]
([(0,5),(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5)],7)                         => [6,5,5,5,3,2,2]
([(0,5),(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6)],7)                   => [6,5,5,3,2,2,2,2]
([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)             => [6,5,3,2,2,2,2,2,2]
([(0,5),(0,6),(1,4),(1,6),(2,4),(2,5),(3,4),(3,5),(3,6)],7)                   => [5,5,5,3,2,2,2,2]
([(0,5),(0,6),(1,4),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)             => [5,5,3,2,2,2,2,2,2]
([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)       => [5,3,2,2,2,2,2,2,2,2]
([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => [3,2,2,2,2,2,2,2,2,2,2]
([(0,6),(1,5),(1,6),(2,4),(2,5),(3,4),(3,5),(4,6)],7)                         => [18,2,2,2,2]
([(0,5),(0,6),(1,4),(1,6),(2,4),(2,6),(3,5),(4,3)],7)                         => [13,2,2]
([(0,4),(1,4),(2,5),(2,6),(3,5),(3,6),(4,3)],7)                               => [5,4,2,2,2]
([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(6,2),(6,3)],7)                         => [5,2,2,2]
([(0,5),(1,5),(2,4),(2,6),(3,4),(3,6),(5,6)],7)                               => [8,6,6,3,2,2]
([(0,5),(0,6),(1,5),(1,6),(2,4),(3,4),(4,5),(4,6)],7)                         => [7,6,2,2,2,2,2]
([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(3,6)],7)                               => [8,6,6,3,2,2,2,2,2]
([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)                         => [6,6,5,3,2,2,2,2,2,2]
([(0,6),(1,4),(1,5),(2,4),(2,5),(3,6),(5,3)],7)                               => [11,5,2,2]
([(0,5),(0,6),(1,5),(1,6),(2,4),(3,4),(6,2),(6,3)],7)                         => [5,4,2,2,2]
([(0,3),(1,5),(1,6),(2,5),(2,6),(4,3),(5,4),(6,4)],7)                         => [5,4,2,2,2,2]
([(0,5),(0,6),(1,5),(1,6),(2,4),(3,4),(5,3),(6,2)],7)                         => [5,3,3,2]
([(0,5),(0,6),(1,5),(1,6),(2,3),(4,3),(5,4),(6,2),(6,4)],7)                   => [5,5,2]
([(0,5),(0,6),(1,5),(1,6),(3,2),(4,2),(5,3),(5,4),(6,3),(6,4)],7)             => [5,2,2,2]
([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(5,6)],7)                               => [10,6,2,2,2,2,2,2,2]
([(0,6),(1,4),(1,5),(2,4),(2,5),(3,6),(4,6),(5,3)],7)                         => [15,2,2]
([(0,4),(0,5),(1,4),(1,5),(2,6),(3,6),(4,6),(5,2),(5,3)],7)                   => [8,2,2,2]
([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7)                         => [7,6,2,2,2,2,2,2,2,2]
([(0,6),(1,5),(2,3),(2,5),(4,6),(5,4)],7)                                     => [10,7,5]
([(0,6),(1,2),(1,6),(3,5),(4,5),(6,3),(6,4)],7)                               => [7,5,2,2]
([(0,6),(1,6),(2,5),(3,4),(3,5),(5,6)],7)                                     => [18,10,6]
([(0,6),(1,6),(2,4),(3,5),(5,6)],7)                                           => [21,6,6,6]
([(0,6),(1,6),(2,3),(3,6),(4,5),(6,4)],7)                                     => [9,6]
([(0,6),(1,6),(2,5),(3,4),(4,6),(6,5)],7)                                     => [15,6,6]
([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7)                                     => [7,6,6,6,6,6]
([(0,6),(1,5),(2,5),(3,4),(4,6)],7)                                           => [21,14]
([(0,6),(1,6),(2,5),(3,4),(4,5),(6,3)],7)                                     => [11,2,2]
([(0,5),(1,5),(2,3),(3,6),(4,6),(5,4)],7)                                     => [13,6]
([(0,6),(1,6),(2,5),(3,5),(4,3),(6,2),(6,4)],7)                               => [9,2]
([(0,5),(1,5),(2,4),(3,6),(4,6),(5,3),(5,4)],7)                               => [11,2,2]
([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)                                     => [7,6,6,6,6]
([(0,6),(1,6),(2,5),(3,4),(4,5),(4,6)],7)                                     => [14,7,5,5]
([(0,6),(1,5),(2,3),(3,6),(4,5),(6,4)],7)                                     => [9,8]
([(0,6),(1,2),(2,6),(3,5),(4,5),(6,3),(6,4)],7)                               => [9,2]
([(0,6),(1,6),(2,5),(3,4),(4,5),(5,6)],7)                                     => [15,14]
([(3,6),(4,5)],7)                                                             => [6,6,6,6,6,6,6,6,6,6,6,6]
([(3,6),(4,5),(4,6)],7)                                                       => [10,10,10,10,6,6,6,6]
([(2,6),(3,4),(3,6),(4,5)],7)                                                 => [8,8,8,8,6,6]
([(1,6),(2,3),(2,6),(3,4),(3,5)],7)                                           => [8,8,6,6,6]
([(0,6),(1,5),(1,6),(5,2),(5,3),(5,4)],7)                                     => [8,6,6,6,3]
([(0,6),(1,4),(1,6),(4,2),(4,3),(4,5),(6,5)],7)                               => [6,4,4,4,3]
([(0,6),(1,3),(1,6),(3,2),(3,4),(3,5),(6,4),(6,5)],7)                         => [6,4,3,2,2]
([(0,6),(1,2),(1,6),(2,3),(2,4),(2,5),(6,3),(6,4),(6,5)],7)                   => [5,4,2,2,2]
([(1,5),(2,3),(2,5),(3,4),(3,6),(5,6)],7)                                     => [6,6,6,4,4]
([(1,4),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7)                               => [10,4,4,2,2]
([(0,5),(1,4),(1,5),(4,3),(4,6),(5,6),(6,2)],7)                               => [12,3]
([(0,6),(1,5),(1,6),(5,2),(5,3),(6,4)],7)                                     => [10,4,4,4]
([(0,6),(1,4),(1,6),(4,3),(4,5),(6,2),(6,5)],7)                               => [6,6,4,2]
([(0,6),(1,3),(1,6),(3,4),(3,5),(6,2),(6,4),(6,5)],7)                         => [8,4,2,2]
([(2,5),(3,4),(3,5),(4,6),(5,6)],7)                                           => [10,10,4,4,4,4]
([(1,5),(2,3),(2,5),(3,6),(5,6),(6,4)],7)                                     => [10,10]
([(0,5),(1,4),(1,5),(4,6),(5,6),(6,2),(6,3)],7)                               => [5,5,2]
([(1,6),(2,3),(2,6),(3,5),(6,4)],7)                                           => [10,10,4,4]
([(1,5),(2,3),(2,5),(3,6),(5,4),(5,6)],7)                                     => [8,8,4,4]
([(0,6),(1,5),(1,6),(5,2),(6,3),(6,4)],7)                                     => [10,6,4]
([(0,6),(1,4),(1,6),(4,5),(6,2),(6,3),(6,5)],7)                               => [8,6,4]
([(1,6),(2,3),(2,6),(3,5),(5,4)],7)                                           => [18,10]
([(1,5),(2,3),(2,5),(3,4),(4,6),(5,6)],7)                                     => [18,6]
([(0,5),(1,4),(1,5),(3,6),(4,3),(5,6),(6,2)],7)                               => [10,3]
([(0,6),(1,5),(1,6),(4,2),(5,4),(6,3)],7)                                     => [10,4,4]
([(0,6),(1,3),(1,6),(3,5),(5,4),(6,2),(6,5)],7)                               => [14]
([(0,6),(1,4),(1,6),(3,5),(4,3),(6,2),(6,5)],7)                               => [16]
([(0,6),(1,4),(1,6),(4,5),(5,2),(5,3)],7)                                     => [9,6,5]
([(0,6),(1,3),(1,6),(3,4),(4,2),(4,5),(6,5)],7)                               => [16]
([(0,6),(1,2),(1,6),(2,3),(3,4),(3,5),(6,4),(6,5)],7)                         => [9,3,2]
([(3,5),(3,6),(4,5),(4,6)],7)                                                 => [6,6,6,6,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2]
([(2,5),(2,6),(3,5),(3,6),(6,4)],7)                                           => [14,14,2,2,2,2]
([(1,5),(1,6),(2,5),(2,6),(6,3),(6,4)],7)                                     => [14,2,2,2,2,2,2]
([(0,5),(0,6),(1,5),(1,6),(6,2),(6,3),(6,4)],7)                               => [7,2,2,2,2,2,2,2]
([(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7)                                     => [4,4,4,4,2,2,2,2,2,2,2,2]
([(1,4),(1,5),(2,4),(2,5),(4,6),(5,6),(6,3)],7)                               => [10,2,2,2,2]
([(1,5),(1,6),(2,5),(2,6),(5,4),(6,3)],7)                                     => [6,6,4,4,2,2]
([(1,4),(1,6),(2,4),(2,6),(4,5),(6,3),(6,5)],7)                               => [10,4,4,2,2]
([(1,5),(1,6),(2,5),(2,6),(5,3),(5,4),(6,3),(6,4)],7)                         => [4,4,2,2,2,2,2,2]
([(0,5),(0,6),(1,5),(1,6),(5,4),(6,2),(6,3)],7)                               => [6,4,3,3,2]
([(0,5),(0,6),(1,5),(1,6),(5,4),(6,2),(6,3),(6,4)],7)                         => [6,5,4,2]
([(0,5),(0,6),(1,5),(1,6),(5,3),(5,4),(6,2),(6,4)],7)                         => [8,4,2,2]
([(0,5),(0,6),(1,5),(1,6),(5,3),(5,4),(6,2),(6,3),(6,4)],7)                   => [5,4,2,2,2]
([(0,5),(0,6),(1,5),(1,6),(5,2),(5,3),(5,4),(6,2),(6,3),(6,4)],7)             => [4,2,2,2,2,2]
([(1,5),(1,6),(2,5),(2,6),(3,4)],7)                                           => [6,6,6,6,6,6,6]
([(1,6),(2,4),(2,5),(3,4),(3,5),(3,6)],7)                                     => [8,8,6,6,6,2,2]
([(0,4),(1,5),(1,6),(2,4),(2,5),(2,6),(6,3)],7)                               => [14,9,2]
([(0,4),(1,5),(1,6),(2,4),(2,5),(2,6),(5,3),(6,3)],7)                         => [8,6,6,2]
([(0,6),(1,4),(1,5),(2,4),(2,5),(2,6),(5,3),(6,3)],7)                         => [11,8,2]
([(0,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7)                   => [8,6,4,2]
([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)                               => [10,6,6,6,2,2,2,2]
([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(5,3)],7)                         => [14,6,2,2]
([(0,6),(1,3),(1,4),(1,6),(2,3),(2,4),(2,6),(3,5),(4,5)],7)                   => [8,6,3,2,2]
([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7)             => [6,5,4,2,2]
([(0,6),(1,3),(1,4),(1,6),(2,3),(2,4),(2,6),(4,5),(6,5)],7)                   => [11,5,2,2]
([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(6,3)],7)                         => [10,4,4,2,2]
([(0,6),(1,4),(1,5),(2,4),(2,5),(2,6),(6,3)],7)                               => [8,6,4,4,2]
([(1,5),(1,6),(2,5),(2,6),(3,4),(6,3)],7)                                     => [10,4,4,2,2]
([(0,5),(0,6),(1,5),(1,6),(4,3),(5,4),(6,2)],7)                               => [13,2]
([(0,5),(0,6),(1,5),(1,6),(2,3),(5,4),(6,2),(6,4)],7)                         => [9,3,2]
([(0,5),(0,6),(1,5),(1,6),(4,2),(5,3),(5,4),(6,3),(6,4)],7)                   => [8,2,2]
([(0,5),(0,6),(1,5),(1,6),(2,4),(5,2),(5,3),(6,3),(6,4)],7)                   => [11,2]
([(0,5),(0,6),(1,5),(1,6),(4,3),(5,4),(6,2),(6,4)],7)                         => [11,2]
([(0,5),(0,6),(1,5),(1,6),(3,4),(5,3),(6,2),(6,4)],7)                         => [9,3,2]
([(1,6),(2,4),(2,5),(3,4),(3,5),(5,6)],7)                                     => [10,10,2,2,2,2,2,2]
([(1,4),(1,5),(2,4),(2,5),(3,6),(4,6),(5,3)],7)                               => [8,8,2,2]
([(1,6),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7)                               => [14,2,2,2,2,2,2,2,2]
([(0,6),(1,4),(1,5),(2,4),(2,5),(4,6),(5,6),(6,3)],7)                         => [8,2,2,2,2]
([(0,5),(1,4),(1,6),(2,4),(2,6),(4,5),(6,3)],7)                               => [11,3,3,2,2]
([(0,6),(1,4),(1,5),(2,4),(2,5),(4,6),(5,3),(5,6)],7)                         => [11,5,2,2]
([(0,6),(1,4),(1,5),(2,4),(2,5),(5,6),(6,3)],7)                               => [8,4,2,2,2]
([(0,4),(1,5),(1,6),(2,5),(2,6),(4,3),(5,4),(6,3)],7)                         => [11,2,2,2]
([(0,5),(0,6),(1,5),(1,6),(2,4),(6,3)],7)                                     => [21,6]
([(0,5),(0,6),(1,5),(1,6),(4,3),(6,2),(6,4)],7)                               => [15,2]
([(0,5),(0,6),(1,5),(1,6),(3,4),(5,2),(5,3),(6,4)],7)                         => [11,2,2]
([(0,5),(1,4),(1,6),(2,4),(2,6),(6,3),(6,5)],7)                               => [18,2,2]
([(0,4),(0,5),(1,4),(1,5),(2,3),(4,6),(5,6)],7)                               => [12,6,6]
([(0,4),(1,5),(1,6),(2,5),(2,6),(5,3),(6,3),(6,4)],7)                         => [13,2,2,2]
([(0,6),(1,3),(1,4),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7)                   => [10,2,2,2,2]
([(1,5),(1,6),(2,5),(2,6),(3,4),(3,6)],7)                                     => [8,8,6,6,6,2,2]
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,6),(6,4)],7)                               => [7,6,5,5]
([(1,5),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5)],7)                               => [10,10,2,2,2,2]
([(0,5),(0,6),(1,4),(1,6),(2,4),(2,6),(4,5),(6,3)],7)                         => [6,4,3,2,2]
([(0,5),(0,6),(1,4),(1,6),(2,4),(2,6),(4,5),(5,3)],7)                         => [7,5,2,2]
([(0,3),(0,6),(1,3),(1,6),(2,5),(2,6),(3,5),(5,4),(6,4)],7)                   => [11,2,2]
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,6),(5,4)],7)                               => [15,6,3]
([(0,4),(0,6),(1,4),(1,6),(2,3),(2,6),(4,5),(6,5)],7)                         => [13,6,2]
([(0,5),(0,6),(1,5),(1,6),(2,4),(2,6),(5,3),(5,4)],7)                         => [13,2,2,2]
([(0,3),(0,6),(1,3),(1,6),(2,4),(2,6),(3,4),(3,5),(6,5)],7)                   => [8,4,2,2]
([(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6)],7)                               => [10,6,6,6,2,2,2,2]
([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(6,3)],7)                         => [9,7,6]
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,5),(2,6),(5,4),(6,4)],7)                   => [10,6,2,2]
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4)],7)                         => [8,6,4,4,3]
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(6,4)],7)                   => [7,6,5,2]
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7)             => [6,5,4,2,2]
([(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(4,6)],7)                               => [10,10,6,6]
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,5),(3,6),(5,4)],7)                         => [6,6,4,3]
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,5),(3,6),(5,4),(6,4)],7)                   => [11,6]
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,5),(3,6),(6,4)],7)                         => [7,6,5]
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,6),(3,4)],7)                               => [15,4,4,3]
([(0,4),(0,6),(1,4),(1,6),(2,3),(2,6),(3,5),(6,5)],7)                         => [13,6,2]
([(0,4),(0,6),(1,4),(1,6),(2,3),(2,6),(3,5),(4,5)],7)                         => [8,7,6]
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,5),(3,6),(4,6),(5,6)],7)                   => [8,6,4,2]
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,5),(3,4),(3,6)],7)                         => [13,4,4,2]
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,5),(3,4),(3,6),(5,4)],7)                   => [8,6,4]
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,5),(3,4),(4,6)],7)                         => [13,4,4]
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4)],7)                                     => [6,6,6,3,3,3,2,2,2,2]
([(0,5),(0,6),(1,5),(1,6),(4,2),(4,3),(6,4)],7)                               => [5,4,2,2,2]
([(0,5),(0,6),(1,5),(1,6),(4,2),(4,3),(5,4),(6,4)],7)                         => [5,2,2,2]
([(0,5),(0,6),(1,5),(1,6),(3,2),(3,4),(5,3),(6,4)],7)                         => [11,2]
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(5,2),(6,3),(6,4)],7)                   => [8,2,2]
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,6),(5,6)],7)                               => [16,6,3]
([(0,3),(0,4),(1,5),(1,6),(2,5),(2,6),(6,3),(6,4)],7)                         => [10,2,2,2,2,2]
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,6),(4,6),(5,6)],7)                         => [8,6,6,3]
([(0,3),(0,4),(1,5),(1,6),(2,5),(2,6),(5,4),(6,3)],7)                         => [8,7,2,2]
([(0,5),(0,6),(1,3),(1,4),(2,3),(2,4),(3,6),(4,5),(4,6)],7)                   => [7,5,2,2,2]
([(0,5),(0,6),(1,3),(1,4),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7)             => [7,2,2,2,2,2]
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,6)],7)                               => [8,6,6,3,2,2,2,2,2]
([(0,4),(0,6),(1,4),(1,6),(2,3),(2,5),(2,6),(4,5)],7)                         => [17,6]
([(0,3),(0,6),(1,3),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5)],7)                   => [10,2,2,2,2]
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6)],7)                         => [6,6,5,3,2,2,2,2,2,2]
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(4,6)],7)                         => [18,6,2,2]
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(3,6),(4,6)],7)                   => [10,6,6,2,2]
([(0,5),(0,6),(1,2),(1,4),(3,5),(3,6),(4,3)],7)                               => [11,5,2,2]
([(0,3),(0,4),(1,5),(1,6),(2,5),(2,6),(4,1),(4,2)],7)                         => [5,4,2,2,2,2]
([(0,3),(0,4),(1,5),(1,6),(2,5),(2,6),(3,2),(4,1)],7)                         => [5,3,3,2]
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(4,6)],7)                               => [16,6,3,2,2]
([(0,4),(0,6),(1,4),(1,6),(2,3),(2,5),(3,6),(4,5)],7)                         => [10,6,4]
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(4,5),(4,6)],7)                         => [10,6,2,2,2,2,2]
([(0,5),(0,6),(1,3),(1,4),(2,5),(2,6),(3,5),(3,6),(4,2)],7)                   => [15,2]
([(0,3),(0,4),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,1),(4,2)],7)             => [8,2,2,2]
([(0,5),(0,6),(1,2),(1,4),(2,6),(3,5),(3,6),(4,3)],7)                         => [18]
([(0,3),(0,4),(1,5),(1,6),(2,5),(2,6),(3,6),(4,1),(4,2)],7)                   => [11,2,2]
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(3,6),(4,6)],7)                         => [8,6,6,3,2,2]
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(3,6),(4,5)],7)                         => [8,7,6,2,2]
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(3,6),(4,5),(4,6)],7)                   => [7,6,5,2,2,2]
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7)             => [7,6,2,2,2,2,2]
([(1,5),(1,6),(2,5),(2,6),(3,4),(4,6)],7)                                     => [8,8,6,6,6]
([(0,5),(0,6),(1,5),(1,6),(2,3),(3,6),(6,4)],7)                               => [6,5,5,3]
([(0,5),(0,6),(1,5),(1,6),(2,3),(3,6),(5,4)],7)                               => [7,6,4,4]
([(0,4),(0,6),(1,4),(1,6),(2,3),(3,6),(4,5),(6,5)],7)                         => [9,6,3]
([(1,5),(1,6),(2,5),(2,6),(3,4),(4,5),(4,6)],7)                               => [14,6,6,2,2]
([(0,5),(0,6),(1,5),(1,6),(2,4),(4,5),(4,6),(6,3)],7)                         => [11,6]
([(0,5),(0,6),(1,5),(1,6),(2,3),(3,5),(3,6),(5,4),(6,4)],7)                   => [8,6,2]
([(0,5),(0,6),(1,5),(1,6),(2,3),(3,4)],7)                                     => [12,4,4,4,4]
([(0,5),(0,6),(1,5),(1,6),(3,4),(4,2),(6,3)],7)                               => [11,2]
([(0,5),(0,6),(1,5),(1,6),(2,3),(4,2),(5,4),(6,4)],7)                         => [6,2,2]
([(0,5),(0,6),(1,5),(1,6),(3,4),(4,2),(5,3),(6,4)],7)                         => [9,2]
([(0,5),(0,6),(1,5),(1,6),(2,3),(3,4),(5,2),(6,4)],7)                         => [6,4,2]
([(0,4),(0,5),(1,4),(1,5),(2,3),(3,6),(5,6)],7)                               => [11,6,3,3]
([(0,4),(0,5),(1,4),(1,5),(2,3),(3,6),(4,6),(5,6)],7)                         => [6,6,4,3,3]
([(0,5),(0,6),(1,4),(3,5),(3,6),(4,2),(4,3)],7)                               => [8,4,2,2,2]
([(0,4),(2,5),(2,6),(3,5),(3,6),(4,1),(4,2),(4,3)],7)                         => [8,2,2,2,2]
([(0,5),(0,6),(1,5),(1,6),(2,3),(3,4),(3,6)],7)                               => [8,6,4,4,2]
([(0,4),(0,6),(1,4),(1,6),(2,3),(3,5),(3,6),(4,5)],7)                         => [6,6,4,3]
([(0,5),(0,6),(1,5),(1,6),(2,3),(3,4),(3,5),(3,6)],7)                         => [10,4,4,2,2]
([(0,5),(0,6),(1,5),(1,6),(2,3),(3,4),(3,6),(4,5)],7)                         => [7,5,4,4]
([(0,5),(0,6),(1,5),(1,6),(2,3),(3,4),(4,6)],7)                               => [9,5,4,4]
([(0,5),(0,6),(1,4),(2,6),(3,5),(3,6),(4,2),(4,3)],7)                         => [5,5,4,2]
([(0,4),(1,6),(2,5),(2,6),(3,5),(3,6),(4,1),(4,2),(4,3)],7)                   => [5,5,2,2]
([(0,5),(0,6),(1,5),(1,6),(2,3),(3,4),(4,5),(4,6)],7)                         => [5,4,4,4,2]
([(0,5),(0,6),(1,4),(2,5),(2,6),(3,5),(3,6),(4,2),(4,3)],7)                   => [5,4,2,2,2]
([(0,4),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,1),(4,2),(4,3)],7)             => [5,2,2,2,2]
([(2,6),(3,4),(3,6),(6,5)],7)                                                 => [10,10,10,10]
([(1,6),(2,3),(2,6),(6,4),(6,5)],7)                                           => [10,10,2,2,2,2]
([(0,6),(1,2),(1,6),(6,3),(6,4),(6,5)],7)                                     => [10,2,2,2,2,2,2]
([(2,6),(3,4),(3,5)],7)                                                       => [6,6,6,6,6,6,6,6,6,6]
([(2,6),(3,4),(3,5),(3,6)],7)                                                 => [10,10,6,6,6,6,6,6]
([(1,6),(2,3),(2,4),(2,6),(4,5)],7)                                           => [14,14,6,6]
([(0,6),(1,4),(1,5),(1,6),(5,2),(5,3)],7)                                     => [14,6,6,6]
([(0,6),(1,3),(1,4),(1,6),(4,2),(4,5),(6,5)],7)                               => [18,6]
([(0,6),(1,2),(1,3),(1,6),(3,4),(3,5),(6,4),(6,5)],7)                         => [11,5,2,2]
([(1,5),(2,3),(2,4),(2,5),(4,6),(5,6)],7)                                     => [22,10]
([(0,5),(1,3),(1,4),(1,5),(4,6),(5,6),(6,2)],7)                               => [8,5,5]
([(0,6),(1,3),(1,5),(1,6),(5,2),(6,4)],7)                                     => [26]
([(0,6),(1,3),(1,4),(1,6),(4,5),(6,2),(6,5)],7)                               => [22]
([(1,5),(2,3),(2,4),(2,5),(3,6),(4,6)],7)                                     => [8,8,6,6,6]
([(1,5),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7)                               => [10,6,6,4,4]
([(0,5),(1,2),(1,3),(1,5),(2,6),(3,6),(5,6),(6,4)],7)                         => [6,5,5]
([(0,6),(1,3),(1,4),(1,6),(3,5),(4,5),(6,2)],7)                               => [10,4,4,4]
([(0,5),(1,2),(1,3),(1,5),(2,6),(3,6),(5,4),(5,6)],7)                         => [8,4,4,4]
([(0,5),(1,3),(1,4),(1,5),(3,6),(4,6),(6,2)],7)                               => [9,6,5]
([(0,6),(1,2),(1,3),(1,6),(2,5),(3,5),(5,4),(6,4)],7)                         => [9,6,3]
([(0,6),(1,4),(1,5),(1,6),(4,3),(5,2)],7)                                     => [8,3,3,3,3,3,3,3]
([(0,6),(1,3),(1,4),(1,6),(3,5),(4,2),(4,5)],7)                               => [15,8,3]
([(0,6),(1,2),(1,3),(1,6),(2,5),(3,4),(3,5),(6,4)],7)                         => [13,4,3]
([(0,4),(1,2),(1,3),(1,4),(2,6),(3,5),(3,6),(4,5),(4,6)],7)                   => [9,5,4]
([(0,5),(1,3),(1,4),(1,5),(3,6),(4,2),(4,6),(5,6)],7)                         => [12,6,4]
([(0,6),(1,2),(1,3),(1,6),(2,4),(2,5),(3,4),(3,5)],7)                         => [8,6,6,3]
([(0,4),(1,2),(1,3),(1,4),(2,5),(2,6),(3,5),(3,6),(4,6)],7)                   => [6,6,4,3]
([(0,4),(1,2),(1,3),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)             => [6,5,4,2]
([(0,6),(1,3),(1,4),(1,6),(3,5),(4,2),(6,5)],7)                               => [19,4]
([(0,6),(1,2),(1,3),(1,6),(2,5),(3,4),(6,4),(6,5)],7)                         => [5,5,5,4]
([(1,6),(2,3),(2,4),(2,6),(6,5)],7)                                           => [10,10,4,4,4,4]
([(0,6),(1,2),(1,3),(1,6),(6,4),(6,5)],7)                                     => [10,4,4,2,2,2,2]
([(1,6),(2,3),(2,4),(2,5)],7)                                                 => [6,6,6,6,6,6,6,6,6]
([(1,6),(2,3),(2,4),(2,5),(2,6)],7)                                           => [10,6,6,6,6,6,6,6]
([(0,6),(1,3),(1,4),(1,5),(1,6),(5,2)],7)                                     => [14,6,6,6,6]
([(0,6),(1,2),(1,3),(1,4),(1,6),(4,5),(6,5)],7)                               => [14,11,5]
([(0,6),(1,2),(1,3),(1,4),(1,6),(3,5),(4,5)],7)                               => [14,6,6,6]
([(0,5),(1,2),(1,3),(1,4),(1,5),(3,6),(4,6),(5,6)],7)                         => [11,6,6,5]
([(0,5),(1,2),(1,3),(1,4),(1,5),(2,6),(3,6),(4,6)],7)                         => [8,6,6,6,3]
([(0,5),(1,2),(1,3),(1,4),(1,5),(2,6),(3,6),(4,6),(5,6)],7)                   => [6,6,6,5,4]
([(0,6),(1,2),(1,3),(1,4),(1,6),(6,5)],7)                                     => [10,4,4,4,4,4,4]
([(0,6),(1,2),(1,3),(1,4),(1,5)],7)                                           => [6,6,6,6,6,6,6,3,3,3]
([(0,6),(1,2),(1,3),(1,4),(1,5),(1,6)],7)                                     => [6,6,6,6,6,6,6,5,3]
([(0,2),(0,3),(0,4),(0,6),(5,1),(6,5)],7)                                     => [5,4,4,4,4,4,4,4]
([(0,6),(1,2),(1,3),(1,4),(1,5),(5,6)],7)                                     => [10,6,6,6,2,2,2,2,2,2,2]
([(0,2),(0,3),(0,4),(0,5),(1,6),(4,6),(5,1)],7)                               => [15,14]
([(0,6),(1,2),(1,3),(1,4),(1,5),(4,6),(5,6)],7)                               => [10,6,2,2,2,2,2,2,2,2,2,2,2]
([(0,2),(0,3),(0,4),(0,5),(1,6),(3,6),(4,6),(5,1)],7)                         => [15,6,6]
([(0,6),(1,2),(1,3),(1,4),(1,5),(3,6),(4,6),(5,6)],7)                         => [10,2,2,2,2,2,2,2,2,2,2,2,2,2]
([(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,1)],7)                   => [8,6,6,6]
([(0,6),(1,2),(1,3),(1,4),(1,5),(2,6),(3,6),(4,6),(5,6)],7)                   => [7,2,2,2,2,2,2,2,2,2,2,2,2,2,2]
([(0,5),(1,2),(1,3),(1,4),(1,6),(5,6)],7)                                     => [8,4,4,4,4,4,4,3]
([(0,4),(1,2),(1,3),(1,5),(1,6),(4,5),(4,6)],7)                               => [8,4,4,3,2,2,2,2]
([(0,3),(1,2),(1,4),(1,5),(1,6),(3,4),(3,5),(3,6)],7)                         => [8,3,2,2,2,2,2,2]
([(0,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6)],7)                   => [7,2,2,2,2,2,2,2]
([(1,3),(1,4),(1,6),(5,2),(6,5)],7)                                           => [10,4,4,4,4,4,4]
([(0,3),(0,4),(0,5),(5,6),(6,1),(6,2)],7)                                     => [5,4,4,4,2,2,2,2]
([(1,6),(2,3),(2,4),(2,5),(5,6)],7)                                           => [10,10,6,6,2,2,2,2,2,2]
([(0,6),(1,2),(1,3),(1,4),(4,6),(6,5)],7)                                     => [8,4,4,4,2,2,2]
([(1,2),(1,4),(1,5),(3,6),(4,6),(5,3)],7)                                     => [30]
([(0,3),(0,4),(0,5),(1,6),(4,6),(5,1),(6,2)],7)                               => [9,8]
([(1,6),(2,3),(2,4),(2,5),(4,6),(5,6)],7)                                     => [10,10,2,2,2,2,2,2,2,2,2,2]
([(0,6),(1,2),(1,3),(1,4),(3,6),(4,6),(6,5)],7)                               => [8,4,2,2,2,2,2]
([(1,3),(1,4),(1,5),(2,6),(3,6),(4,6),(5,2)],7)                               => [8,8,6,6]
([(0,3),(0,4),(0,5),(1,6),(3,6),(4,6),(5,1),(6,2)],7)                         => [9,6]
([(1,6),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7)                               => [14,2,2,2,2,2,2,2,2,2,2,2,2]
([(0,6),(1,2),(1,3),(1,4),(2,6),(3,6),(4,6),(6,5)],7)                         => [8,2,2,2,2,2,2]
([(0,6),(1,3),(1,4),(1,5),(3,6),(4,6),(5,2)],7)                               => [11,6,6,3,3]
([(0,6),(1,2),(1,3),(1,4),(2,6),(3,6),(4,5),(6,5)],7)                         => [11,2,2,2,2,2]
([(0,3),(0,4),(0,5),(2,6),(3,6),(4,6),(5,1),(5,2)],7)                         => [11,6,2,2,2]
([(0,6),(1,3),(1,4),(1,5),(3,6),(4,6),(5,2),(5,6)],7)                         => [11,6,6,5]
([(0,6),(1,3),(1,4),(1,5),(4,6),(5,2)],7)                                     => [14,6,6,6]
([(0,6),(1,2),(1,3),(1,4),(3,6),(4,5),(6,5)],7)                               => [18,2,2,2]
([(0,3),(0,4),(0,5),(2,6),(4,6),(5,1),(5,2)],7)                               => [11,10,2,2]
([(0,6),(1,3),(1,4),(1,5),(4,6),(5,2),(5,6)],7)                               => [14,10,6]

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Created: Jul 13, 2023 at 15:54 by Martin Rubey

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Last Updated: Jul 13, 2023 at 15:54 by Martin Rubey